To a degree, the drop in support she experienced this fall can be seen as self-perpetuating: Some less-ideological voters got behind her in the late summer and early fall, when she was increasingly being seen as a front-runner. As questions took hold about her viability against President Trump in a general election and how she would fund her proposal for a “Medicare for all”-type health care system, some of those supporters defected to other top candidates, such as Mr. Biden and Mr. Buttigieg.

In Iowa, where Ms. Warren seemed to have an edge, Mr. Buttigieg has pulled ahead in most polls. Both candidates have staked much of their momentum on this first-voting state, and both have opened more than 20 campaign offices there. As Mr. Buttigieg has emerged as the leader of the pack in Iowa, he has argued that he will be able to appeal to potential swing voters in a general election.

Indeed, many Democrats this year say they are driven by an almost single-minded desire to unseat Mr. Trump. In various polls, Democratic voters have indicated that finding a candidate who can defeat the president next November matters to them more than nominating one whose policies gibe with their own views.

Nationwide, it is Mr. Biden who is generally seen as the most capable of doing that, though most of the leading Democratic candidates, including Ms. Warren, come out ahead in potential match-ups with Mr. Trump. A Gallup poll last month found that 51 percent of Democrats said they viewed Mr. Biden as the potential nominee with the greatest chance of beating Mr. Trump. Mr. Sanders and Ms. Warren were locked in a virtual tie for a distant second place, with 16 percent and 15 percent each.

“For a big chunk of the Democratic electorate, the goal of this election is to have a Democrat who can beat Trump,” Mr. McElwee said, adding that head-to-head polls showing Ms. Warren performing slightly worse than Mr. Biden and Mr. Sanders against the president have contributed to her decline. But he cautioned against reading too deeply into the current trends.

“I think Warren actually still has shown that, yes, she has a lot of supporters who are quite fluid, but there’s still a chance in the next two months she can solidify those voters,” he said.