Trump roars back on Twitter.

President Trump, who was overseas at an economic forum, remained uncharacteristically quiet during the first 11 hours of the trial on Tuesday. But as the proceedings reached midnight in Washington, and 6 a.m. in Davos, Switzerland, where the president was, his Twitter feed roared back to life.

From the snowy Alps, Mr. Trump began blitzing out messages at a frenzied pace, reposting tweets, one after another, from Republican allies and friendly commentators in the news media defending him and attacking the House managers, aiming arrows at the trial half a world away.

He pushed out more than 40 tweets in as many minutes, recirculating messages asserting that he did nothing wrong and accusing Democrats of lying about him and depriving him of due process. Among those that he reposted was one from his son Donald Trump Jr. assailing one of the House managers, Representative Adam B. Schiff, saying, “this clown has 0 credibility!”

The Senate blocked another amendment by Democrats along a 53-to-47 party-line vote, this time with Republicans opposing a measure that would have forced President Trump’s defense team to provide documents that Democrats had sought if the president’s lawyers tried to introduce new evidence into the trial record.

The measure, Democrats insisted, would have prevented the selective admission of evidence by Mr. Trump’s team.

Republican senators blocked a Democratic amendment on Tuesday that would have subpoenaed Michael P. Duffey, a White House budget office official, and Robert B. Blair, a top adviser to the White House chief of staff, who was closely involved in the decision over the summer to freeze almost $400 million in military aid for Ukraine. The party-line vote, 53 to 47, stymied the latest attempt by Democrats to guarantee witness testimony as part of the trial.

Mr. Blair defied a subpoena from House impeachment investigators in the fall, but news reports since then have suggested he would be a valuable witness. He helped enact Mr. Trump’s order on the aid freeze, and he listened in real time to a July 25 phone call between President Trump and the leader of Ukraine that is at the center of the case. “Expect Congress to become unhinged,” Mr. Blair warned in one email reported by The New York Times, anticipating the reaction if the White House blocked the aid, which had been approved by Congress.

Mr. Duffey is a Trump appointee who played a notable role in enforcing the president’s freeze over the summer on the military aid for Ukraine. Career nonpartisan government officials testified that his involvement was unusual, but under White House orders, Mr. Duffey defied a subpoena from House investigators for testimony.

The Senate again voted on Tuesday to reject a Democratic effort to subpoena documents and communications related to charges against the president in yet another party-line vote, this time over records from the Defense Department.

Democrats are particularly interested in correspondence between the administration’s budget office and the Defense Department. In an August email released by the administration in a Freedom of Information Act lawsuit, Michael Duffey, a top budget official, wrote to the Defense Department’s acting comptroller and said there was “Clear direction from POTUS to continue to hold” the military aid Congress had appropriated to Ukraine.

It is the fifth Democratic-led amendment the Senate has rejected. Democrats have so far failed to compel the Senate to subpoena documents from the White House, the State Department and the Office of Management and Budget, as well as testimony from the acting White House chief of staff, Mick Mulvaney.

With no end in sight for the debate over amendments, senators appeared to be growing more frustrated with the limitations of the trial. As the Senate reconvened, about a third of its members were late to return, straggling into the chamber.

An aide to Senator Cory Booker tweeted a picture of staff aides carrying 10 large pizzas into the Senate — an indication that people were readying for the long night to continue.

An attempt to strike a deal to shorten debate over whether the Senate should hear testimony from top administration officials and subpoena new documents quickly went nowhere late Tuesday night as Democrats indicated they would continue their efforts to compel new information.

The Senate took a brief break after Senator Mitch McConnell of Kentucky, the majority leader, asked that Senator Chuck Schumer of New York, the Democratic leader, bundle his amendments requesting witnesses and documents into a single package. Such a move would have allowed the Senate to debate and vote on the requests once, instead of individually.

Mr. Schumer seemed open to striking some sort of deal, but when the leaders returned from the break, no deal had been reached, according to aides with knowledge of the discussions, and it appeared that Democrats would press on.

Senator Mitch McConnell of Kentucky, the majority leader, requested that Democrats bundle their amendments so senators would not have to debate each one for hours given “a certain similarity to all” of the measures.

Senator Chuck Schumer of New York, the Democratic leader, responded that he would not force senators to vote on Tuesday night on each amendment he had planned.

“But we will not back off on getting votes on all of these amendments, which we regard as extremely significant,” Mr. Schumer said. Senators are now taking a break, as the two leaders try to determine the floor schedule for the rest of the evening.

Senate Republicans blocked a Democratic attempt on Tuesday to issue a subpoena summoning Mick Mulvaney, the acting White House chief of staff, to testify in President Trump’s impeachment trial. The 53-to-47 vote, which fell along party lines, was the latest effort by Democrats to force the inclusion of new evidence in the proceeding.

Mr. Mulvaney could still be summoned later under Republicans’ proposed rules, but only after opening arguments and a period in which senators can ask questions of the House managers and president’s lawyers is complete. House Democrats subpoenaed Mr. Mulvaney in the fall during their inquiry, but he defied the order. Any similar attempt by the Senate is likely to set off a legal battle with the White House.

Few witnesses have greater access to Mr. Trump than Mr. Mulvaney, who serves as a White House gatekeeper and helped enforce Mr. Trump’s order over the summer to freeze almost $400 million in military aid for Ukraine as he pressed the country to investigate his political rivals. At one point, Mr. Mulvaney acknowledged on national TV that the two acts were connected, only to later recant his statement.

After recessing for dinner, Democrats began debate over an amendment to subpoena Mick Mulvaney, the acting White House chief of staff, to testify in President Trump’s impeachment trial.

The push for his testimony raises the larger question of whether any Republican senators will join Democrats in insisting that senior administration officials appear before the Senate and recount what they knew about Mr. Trump’s pressure campaign against Ukraine. But Democrats are particularly interested in hearing from Mr. Mulvaney given his proximity to Mr. Trump and his role in enacting a freeze on vital military aid that Congress had appropriated to go to Ukraine.

“The Senate has always taken its duty to obtain evidence, including witness testimony, seriously,” said Representative Hakeem Jeffries of New York, one of the House impeachment managers. “This is the only way to ensure fundamental fairness for everyone involved.”

While only government-controlled cameras are allowed in the Senate chamber, there is no rule against reporters bringing in a pad and a pencil.

Art Lien, a courtroom sketch artist, will be observing the impeachment trial from the press gallery and capturing scenes that might not appear on television, including senators catching a few winks during debate.

Mr. Lien has primarily covered the Supreme Court since 1976, but this is not his first impeachment. He drew scenes from President Bill Clinton’s trial in 1999.

Senators in President Trump’s impeachment trial have taken a dinner break, briefly putting on pause the acrimonious debate about the rules of the trial. The trial — only the third in history — has been underway for nearly seven hours as Democrats and Republicans wrangled over whether the Senate should seek additional documents and witnesses before both sides present their arguments.

So far, Democrats have failed to compel the Senate to subpoena documents from the White House, the State Department and the Office of Management and Budget. When the senators return, they will resume debate on a Democratic motion to subpoena Mick Mulvaney, the acting White House chief of staff.

At 7:30 p.m., Senator Mitch McConnell of Kentucky, the majority leader, announced a 30-minute break for senators to get dinner, though the lawmakers are likely to take longer than that to return.

The Senate turned back a Democratic effort to subpoena White House budget documents for President Trump’s impeachment trial. The move to table the effort succeeded along party lines, 53 to 47, with Republicans prevailing in the latest in a series of partisan votes to block new evidence demanded by Democrats from coming to light. Republicans had succeeded in tabling two other similar measures.

Democrats had argued that emails among officials at the Office of Management and Budget about the suspension of security aid from Ukraine had already been disclosed through Freedom of Information Act lawsuits. In particular, they noted communications between Michael P. Duffey, the associate director of the agency, and the Defense Department, in which Mr. Duffey requested that the Pentagon “hold off” on additional aid to Ukraine and to keep the information “closely held.”

The Trump administration had refused House attempts to secure emails and other communications among officials in the budget office and the Defense Department.

The Senate blocked a Democratic attempt on Tuesday to subpoena State Department documents, emails and other correspondence for President Trump’s impeachment trial, including records involving Gordon D. Sondland, the United States ambassador to the European Union. The vote — the second push for documents — was 53 to 47, with the Republican majority prevailing.

Mr. Sondland, a wealthy business executive and Trump donor, told lawmakers that he did not have access to his written records before his testimony in the House impeachment inquiry. Mr. Sondland testified he worked with others to pressure Ukraine “at the express direction of the president” and confirmed that there was a clear “quid pro quo” linking a White House meeting for Ukraine’s president to the investigations Mr. Trump wanted.

The State Department had refused demands by House investigators to turn over documents from Mr. Sondland and other diplomats who testified in the impeachment inquiry. In arguments Tuesday evening, House managers said the documents were essential to fully understand Mr. Trump’s actions. White House lawyers argued that the administration had the right to assert privileges over documents like those from the State Department.

The first party-line defeat, 53 to 47, of a Democratic demand for documents made it clear that Republicans have the votes to hold off Democrats in the impeachment trial for now. So why will Democrats continue to press their case with a series of proposals seemingly destined to lose?

First, Democrats want to show their supporters that they are going to put up a fight and not be dismissed so easily by united Senate Republicans. Democrats have surrendered quickly in the past on other issues and drawn flak from the left.

Second, they want to force Republicans into a series of votes Democrats can then highlight to show the depth of what Democrats will portray as a Republican eagerness to shield President Trump from scrutiny. These votes will no doubt show up in campaign spots this year.

After the Senate voted to block a bid to subpoena White House documents related to President Trump’s pressure campaign on Ukraine, Democrats tried again, mounting a new push to subpoena documents from the State Department.

That amendment, which is likely to be defeated along party lines, would cover a series of communications the administration has withheld, including messages between Secretary of State Mike Pompeo and other senior officials that Democrats say go to the heart of what they knew about Mr. Trump’s pressure campaign on Ukraine.

Representative Val B. Demings of Florida, the first black woman to serve as a House impeachment manager, made her debut speech on the Senate floor, imploring Republicans to support the measure. “We’re talking about a specific, discrete set of materials held by the State Department,” Ms. Demings said.

The Senate voted Tuesday to block a Democratic bid to subpoena White House emails, memos and other documents related to President Trump’s pressure campaign on Ukraine that is at the heart of the impeachment case against him. The vote was 53 to 47 to table the amendment to the trial rules, with Republicans prevailing.

Mr. Trump’s administration refused to provide the documents — including correspondence among the president and his top national security aides — during the House impeachment inquiry. Democrats argued that the documents are necessary for a fair trial that would hold the president accountable.

Republicans have repeatedly said it was the House’s responsibility to gather all the evidence before sending articles of impeachment to the Senate. But the White House stonewalled every request made by the House investigators.

There was a familiar face in the gallery overlooking the Senate chamber on Tuesday: Jeff Flake, the former senator from Arizona who decided not to seek re-election in 2018 after concluding that there was no room in the Republican Party for a critic of President Trump.

Chatting with reporters, Mr. Flake — who also served in the House — said he was not certain whether he would have voted to impeach the president: Good arguments can be made, he said, both for or against the idea that the president’s campaign to pressure Ukraine to investigate his political rivals rose to the level of an impeachable offense.

But one argument that cannot be made, he said, is that Mr. Trump did nothing wrong.

Moments before the Senate reconvened to debate a Democratic amendment this afternoon, Senator Mitch McConnell of Kentucky offered his colleagues a lesson in decorum, Senate-style.

“I’d like to remind everybody to take their seats and when the chief justice comes in we really should all stand,” Mr. McConnell, the majority leader, told senators. The comment was caught on open microphones and broadcast through the Senate press gallery.

Shortly afterward, the cameras clicked on. Chief Justice John G. Roberts Jr. was once again seated at the dais and the senators were in their seats, ready to proceed.

The two people arguing on behalf of Mr. Trump — Jay Sekulow and Pat A. Cipollone — are a contrast in style for a television-focused president. Mr. Cipollone, the low-key White House counsel, has almost no presence on the internet and has barely been photographed since taking on the role. His prominent role on the Senate floor was his first open-to-the-public speaking appearance in a year.

Mr. Sekulow, who helped install Mr. Cipollone in his White House role, has been Mr. Trump’s personal lawyer for nearly three years. Mr. Sekulow is used to talking before an audience, and it showed, as he hammered home points about the investigation by the special counsel, Robert S. Mueller III, and what he argued was a systematic effort to legally ensnare Mr. Trump.

In a significant change, the rules resolution submitted by Senator Mitch McConnell automatically enters the evidence collected by the House impeachment inquiry into the Senate record of the trial, in the same way that a similar resolution treated evidence during the 1999 impeachment trial of former President Bill Clinton.

Democrats had railed against a provision in the proposed rules that would not have automatically admitted into the official record the House’s evidence. They warned that Republicans were attempting to conduct a trial with “no evidence” at all.

The change was hand written into the resolution — one of two changes made before it was introduced to the Senate.

White House lawyers are preparing contingencies for the possibility that witnesses are allowed at the impeachment trial and that John R. Bolton, the former national security adviser, will be called, according to people working with President Trump’s legal team.

Objections to Mr. Bolton’s testimony would most likely involve a combination of arguing that portions of it are classified, and then taking that argument to federal court, according to the people working with the Trump team. They anticipate that such a move might go to the Supreme Court.

The prospect of Mr. Bolton testifying has caused alarm at the White House, even as some officials have played down how much direct knowledge he has about the events related Ukraine aid’s being withheld. Mr. Bolton, though his lawyer, has suggested he had additional relevant information pertaining to the Ukraine matter to share. He also said he was willing to testify.

If there was any doubt that the Senate impeachment trial of President Trump would get bitter and personal, Pat A. Cipollone, the White House counsel, dispelled it quickly.

The arguments on the articles haven’t yet begun. But as he argued on behalf of the trial rules proposed by Republicans, Mr. Cipollone lashed out — personally and directly — at Representative Adam B. Schiff of California, the lead House manager.

“It’s very difficult to listen to Mr. Schiff tell the tale that he just told,” Mr. Cipollone said. Referencing a summary of Mr. Trump’s call with Ukraine’s president Mr. Schiff once gave during a committee hearing — which Mr. Trump frequently mocks — Mr. Cipollone said that Mr. Schiff “manufactured a fraudulent version” of the call. (Mr. Schiff has said that his depiction of the call conferred “the essence” of the presidents’ exchange as a “classic organized crime shakedown.”)

With the Senate sergeant-at-arms uttering the proclamation “All persons are commanded to keep silence, on pain of imprisonment,” the 100 senators are now held to a vow of silence and confined to their chairs for the duration of the day’s proceedings.

As Mr. Cipollone and Mr. Schiff began debating Mr. McConnell’s proposed rules, several senators in the chamber began scribbling notes at their desk, some using large white legal pads while others jotted down notes on the backs of small cards. Most of the desks in the chamber were stocked with pens, pencils and binders.

As they listened, some senators fiddled with pens in their hands while others like Senators Jerry Moran, Republican of Kansas, and Bernie Sanders, Democrat of Vermont, folded their hands as they listened.

Senator Mitch McConnell, the majority leader, made changes to the proposed rules for the trial after Republicans senators, including Susan Collins of Maine, raised concerns about two provisions, according to a spokeswoman for Ms. Collins.

The aide, Annie Clark, said the Maine Republican wanted to ensure that the resolution as closely resembled the rules adopted by the Senate in the 1999 trial of President Bill Clinton as possible.

Mr. McConnell’s initial plans had deviated in several ways from those carried out in Mr. Clinton’s case.

Republicans made last-minute changes in their proposed organizing resolution for the impeachment trial after fierce attacks from Democrats that the proposed rules were unfair and part of an attempted “cover-up” of President Trump’s actions.

The initial proposal, unveiled by Senator Mitch McConnell of Kentucky, the majority leader, had set aside 24 hours for each side to argue the case — but said they had to complete the arguments in two days. Democrats said that would most likely force the debate well into the wee hours of the morning, when few Americans were watching.

When the resolution was read, however, the two-day limit was changed to three days. That would extend the length of the trial by allowing each side to spread their arguments over more, but shorter days.

The White House responded angrily on Tuesday to demands by Democrats that Pat A. Cipollone, the White House counsel, turn over documents relevant to the Ukraine impeachment inquiry — demands that suggest that Mr. Cipollone is intimately involved in the very inquiry for which he is serving as the president’s top lawyer.

Hogan Gidley, the deputy White House press secretary, issued a blistering statement on behalf of Mr. Trump, who is in Davos, Switzerland, attending the World Economic Forum.

“The Democrats are an utter joke — they have no case, and this latest political stunt proves it,” Mr. Gidley said. “The idea that the counsel to the president has to turn over protected documents and confidential information is ludicrous, and to imply he can’t represent the president of the United States in an impeachment proceeding is completely absurd.”

Even before the trial got underway Tuesday, the National Republican Senatorial Committee posted a blistering pro-Trump video on Twitter painting Democrats as an impeachment-hungry mob — a sign that naked partisanship still reigns outside the chamber.

“An angry mob is at the gate, but the United States Senate has the watch,” the announcer intoned gravely, adding, “The sham is over. A fair trial starts now.”

The 2 minute and 17 second video opens with the voices of those shocked by Mr. Trump’s victory in 2016. When Mr. Trump was sworn in, “the left lost it,” the announcer said, as images of a black limousine on fire and riots in the street flickered across the screen.

Senator Mitch McConnell employed one of the oldest tricks in the Senate book to discourage Democrats from mounting time-consuming challenges to his proposed ground rules for the impeachment trial. As the Senate opened Tuesday, Mr. McConnell, the Kentucky Republican and majority leader warned senators that they should be prepared to stay as long as possible to enact a resolution setting the parameters for the trial.

That is a not-so-veiled threat to stay into the wee hours if Democrats offer a long string of proposed changes. Senators are already unhappy with having to sit quietly at their desks with no phones or computers.

Senator Chuck Schumer of New York, the Democratic leader, had already said he would propose a series of changes but promised he would not be dilatory.

The seven House managers submitted one final written brief at noon on Monday, just an hour before the Senate was set to reconvene as a court of impeachment. The 34-page filing included a point-by-point rebuttal of arguments put forward by President Trump’s lawyers in his defense on Monday, and an appeal to senators to convict him based on the House charges.

“President Trump continues to insist that he has done nothing wrong,” the managers wrote. “President Trump’s view that he cannot be held accountable, except in an election he seeks to fix in his favor, underscores the need for the Senate to exercise its solemn constitutional duty to remove President Trump from office.”

The managers asserted that the view put forth by Mr. Trump’s team that abuse of power is not an impeachable office was not only legally and constitutionally “wrong” but “dangerous.” The Constitution, they argued, does not require that an impeachable offense be a crime, and its framers specifically included the impeachment clause to deal with president’s who put their own interests above the country.

Senator Mitch McConnell of Kentucky, the majority leader, in his opening remarks said the day’s proceeding would serve as a critical test for senators.

“This initial step will offer an early signal to our country: Can the Senate still serve our founding purpose?” he said. “Can we still put fairness, evenhandedness and historical precedent ahead of the partisan passions of the day? Today’s vote will contain some answers.”

Mr. McConnell then encouraged senators to support his proposed rules for the trial that have infuriated Democrats, who have described them as tantamount to a “cover-up.” And he again threw cold water on the idea of hearing from new witnesses like John R. Bolton, President Trump’s former national security adviser.