Mr. Biden, a leading contender for the Democratic presidential nomination, planned a midafternoon statement from Wilmington, Del., in which an aide said he would call on Mr. Trump to comply with requests by Congress to investigate the matter, and say that if the president does not, he should be impeached.
Some of his primary rivals went further, saying impeachment should begin, in the words of Senator Elizabeth Warren of Massachusetts, “today.”
The House Judiciary Committee has been conducting its own impeachment investigation focused on the findings of the special counsel, Robert S. Mueller III, as well as allegations that Mr. Trump may be illegally profiting from spending by state and foreign governments, and other matters. But that inquiry has never gotten the imprimatur of a full House vote or the full rhetorical backing of the speaker, as Democrats remained divided about the wisdom and political implications of impeaching a president without broader public support behind them.
What exactly a full impeachment process might look like, if it does go forward, remained unclear early on Tuesday. It may hinge significantly on what comes of a pair of deadlines on Thursday. Democrats have given Joseph Maguire, the acting director of national intelligence, until then to turn over the whistle-blower complaint or risk reprisal. And they have threatened to subpoena the Trump administration for a copy of the transcript of the president’s call with Mr. Zelensky and other relevant documents after Thursday if they are not shared voluntarily.
A select committee would not necessarily grant lawmakers any new fact-finding power. Existing standing committees of the House already have the power to issue subpoenas and set rules of procedure as they see fit. A senior Democratic aide said late Monday that no decision had been made about setting up such a committee. But at least some of Ms. Pelosi’s advisers were pushing for one, arguing that the process would benefit from a small, staff-driven panel that could make a messy political investigation as professional-looking as possible, one of the advisers said on Tuesday.
Creating a special committee would also allow Ms. Pelosi to handpick its Democratic members — a potentially attractive prospect to a speaker who has second-guessed the work of the Judiciary Committee, where impeachment proceedings typically play out. Lawmakers who have discussed the idea routinely raise Mr. Schiff, a close ally of the speaker, as a potential chairman, but senior members of the Judiciary panel are likely to protest any effort to minimize their role.
Whatever Ms. Pelosi and her leadership team decide, it appeared increasingly likely she would face little internal resistance from her caucus, as moderates and progressives, first-term lawmakers and seasoned veterans and others agreed the time had come for to move toward impeachment.