COUNCIL BLUFFS, Iowa — Jackie Wellman worries that Senators Bernie Sanders and Elizabeth Warren are too liberal to defeat President Trump, thinks Mayor Pete Buttigieg of South Bend, Ind., may be too inexperienced and, while she is fond of Joseph R. Biden Jr., she is also uneasy about his tendency to misspeak. “I am worried about the top four candidates because they all have issues,” said Ms. Wellman, a 54-year-old Iowa caucusgoer from West Des Moines who likes Senator Amy Klobuchar.
Ms. Wellman is not the only Democrat who keeps finding flaws as she searches for the best candidate to win the White House.
“Voters are holding back because just when they start to fall in love, they find something that gets them a little nervous,” former Mayor Rahm Emanuel of Chicago said. “The reason it’s so fluid is because they’re still searching for the horse that can win.”
Michael R. Bloomberg believes that may be him. But Mr. Bloomberg’s apparent decision to mount a late entry into the presidential race represents something more than just the robust self-confidence of a New York City billionaire; it’s a manifestation of the Democratic angst that has been growing, particularly among moderate voters and party establishment figures.
Mr. Bloomberg has jolted the Democratic primary, drawing fire from the leading liberals in the field who said he was trying to buy the presidency while posing a direct threat to the centrist candidacy of Mr. Biden. But he has also exposed the jitters among establishment-aligned Democrats who fear that the leftward turn of the party is endangering their chances of building a winning coalition.
For weeks, senior Democratic officials and donors have been musing about whether a new candidate could be lured in the race, a striking illustration of nervousness just three months before the Iowa caucuses. Some talked up Mr. Bloomberg and Hillary Clinton, but others wondered if Senator Sherrod Brown of Ohio might make a late entry to unite a party splintered along ideological lines.
And while some party leaders have muted their concerns in an effort to be neutral, that restraint has started to give way to open expressions of alarm. House Speaker Nancy Pelosi has been repeating the same mantra — “Remember November” — in private about focusing on winning the general election, and has told Democratic allies she was uneasy about a nominee running on Medicare for all.
In an interview last week with Bloomberg News, the San Francisco-based speaker let her concerns slip, saying that creating government-run health care “would increase the vote in my own district, but that’s not what we need to do in order to win the Electoral College.”
Many voters are just as uneasy. “I like Elizabeth Warren,” said Janet Mayo-Smith, 64, who was attending an event for Mr. Biden in Franklin, N.H., on Friday, before adding that she had concerns about whether Ms. Warren was too “radical” to win. She expressed some openness to Mr. Bloomberg, calling him “a good candidate” but also noting that it was late to join the race.
Stanley Brown, 49, also from New Hampshire, called Mr. Bloomberg’s move “interesting.’’ Asked if there were too many voices in the race already, he replied “no such thing.’’
“I’d consider anybody,” he said.
Yet if there is consensus around the high priority of finding the strongest candidate to take on Mr. Trump, there is less agreement among rank-and-file voters that the party needs a white knight to enter the race and rescue them. Interviews with Democrats across four states on Friday showed that many were content to pick from those who remained in the sprawling field.
“I’m not sure what his logic is exactly,” Ricky Hurtado, who attended a Hispanic voters forum in North Carolina that featured Ms. Warren, said of Mr. Bloomberg. Ticking through a number of the leading Democrats in the race, Mr. Hurtado, who is running for the state legislature next year, said, “I think we have enough voices in the primary right now covering the majority of the spectrum in the Democratic Party.”
In New Hampshire, where Mr. Biden and the businessman Andrew Yang were at the statehouse on a frosty day, filing paperwork to be on the state’s primary ballot, voters mostly shrugged about Mr. Bloomberg, with a few grousing about a bloated field getting bigger.
Carolyn Stiles, 75, said she worried that such a large field would make it difficult for Democrats to unify behind one candidate, and described Mr. Bloomberg’s potential entrance into the race as “unhelpful.” She said she was considering Mr. Biden, Ms. Warren and Senator Kamala Harris.
To some center-left Democratic candidates in the race, though, a Bloomberg bid could prove more than unhelpful. Were he to finance a major advertising campaign, he could siphon support, news media attention and ultimately votes from the more moderate candidates, clearing a path for Mr. Sanders and Ms. Warren.
“I don’t know who he hurts but it’s not going to be Bernie or Elizabeth,” said Senator Amy Klobuchar, who is hoping to establish herself in Iowa as a centrist alternative to Mr. Biden. “We don’t need another billionaire,” she added.
Representative Cedric Richmond of Louisiana, a co-chair of Mr. Biden’s campaign, was even blunter.
“It takes a whole lot of moxie to look at the Democratic field and say, ‘None of them can be president and I’ll enter the race and be the savior,’” Mr. Richmond said. “What does Bloomberg offer that’s different? It’s not like he’s 27 — he’s 77.”
Mr. Bloomberg may not prove to be the tonic the party is looking for. His record on policing and economic issues, and his skepticism about the #MeToo movement, could alienate large swaths of the Democratic electorate. And he is choosing an unconventional path in the primary; his advisers signaled Friday that if he runs he’s unlikely to compete in the first four states.
But it is clear enough why he is tempted to run.
Mr. Biden’s unsteady performances in debates and on the campaign trail have undermined confidence in his ability to beat the president. They have hurt Mr. Biden’s fund-raising and early-state polling while exacerbating what may be his biggest liability — that at 76, he may not be nimble enough to beat an unpredictable figure like Mr. Trump. Mr. Buttigieg is gaining support in Iowa, but polls show he has yet to draw any sizable support from nonwhite Democrats.
On the other flank of the party, Democrats are eyeing Mr. Sanders, a 78-year-old democratic socialist who just suffered a heart attack, and Ms. Warren, who is tightening her embrace around a pricey single-payer health care proposal that would terminate private insurance plans.
Both candidates have large and devoted followings, but Democrats have not put forward avowedly liberal presidential nominees in decades; a new New York Times/Siena College poll showing Ms. Warren and Mr. Sanders losing to Mr. Trump in some battleground states only further frayed nerves.
“That frightened a lot of people,” Terry McAuliffe, the former governor of Virginia and D.N.C. chair, said of the survey.
Then came Tuesday’s elections, in which Democrats had great success with mostly moderate candidates who posted large margins in suburban jurisdictions — heightening the conviction among many that the party needed a centrist standard-bearer.
Mr. Bloomberg’s prospective run has mostly agitated Mr. Biden’s supporters, who were already on edge over his fund-raising troubles, his dip in the polls in Iowa and Mr. Trump’s unrelenting assault on him and his son Hunter.
“I don’t like that,” Marge Cudney, who came to celebrate Mr. Biden’s filing for the New Hampshire primary, said of Mr. Bloomberg. “He’s going to divide the team and will weaken everybody. I think he could pull some people away.”
Yet two former lawmakers who are supporting Mr. Biden — Ed Rendell of Pennsylvania and Bob Kerrey, a former senator and governor of Nebraska — spoke favorably about Mr. Bloomberg and said they would be comfortable with him as a candidate if Mr. Biden faltered.
“I’m for Joe,” Mr. Rendell said, “but if something were to happen where Joe was no longer a candidate, which I don’t believe is going to happen, I would enthusiastically consider the mayor as a good strong candidate, and I think he’d make a fine president.”
And not every voter dismissed Mr. Bloomberg, whose advisers believe will be viewed more favorably once Democrats nationally become more familiar with his business career and record as mayor.
Bryant Tolles, 80, of Concord, N.H., gave Mr. Bloomberg high marks for his political experience. “I’m glad he entered the race,” said Mr. Tolles, who is undecided, adding, “They need another centrist who can appeal to the broad electorate.”
For all the heartburn in a party that is often given to indigestion about its presidential field, polls show that Democrats are generally pleased with their options. In a Monmouth University poll released this week, roughly three-quarters of Democratic voters said they were satisfied with the field, while just 16 percent said they were not.
Moderate and conservative Democrats were more likely to say they wished someone new would get in the race, but only 22 percent of them expressed discontent with their choices.
What is more revealing is how many in the party are not yet settled on a candidate: The Times/Siena poll of Iowa, where voters are paying closest attention to the race, found that roughly two-thirds of likely caucusgoers could still be persuaded to change their minds.
The ranks of the undecided include Alan Seabrooke, 89, of Elgin, Iowa, who said, “If you get somebody too far to the left, it scares people.”
Alex Stroda, a 40-year-old from Ottumwa, Iowa, who called himself a “leftist libertarian,” was just as concerned about 2020 but for the opposite reason: He thinks too many of the candidates are not progressive enough.
Mr. Stroda, a former vice chair of the Wapello County Democrats, who is considering Mr. Sanders, Ms. Warren and Mr. Yang, dismissed the logic behind a Bloomberg candidacy.
“This notion that he needs to ride in on a white horse and save the Democratic Party from somebody who is too left-wing,” he said, “is just an extension of the problem we have understanding politics in America, where we have the Democrats tacking to the right as the Republicans tack farther and farther right.”
Sydney Ember reported from Council Bluffs, Iowa, and Jonathan Martin from Washington. Katie Glueck contributed reporting from Franklin, N.H., Matt Stevens from Concord, N.H., Thomas Kaplan from Raleigh, N.C., and Giovanni Russonello from New York City.