Another Sanders supporter, Representative Ilhan Omar of Minnesota, was equally effusive. “I think that would just be the dream of all progressives,” she said. “When you’re going into a battlefield, you want your best players to be on the field starting. And they are our best.”

Centrist Democrats, of course, think just the opposite. Mr. Biden, the former vice president, even after facing intense media scrutiny and racking up a number of self-inflicted errors, still fares slightly better in head-to-head polling against Mr. Trump than either Ms. Warren or Mr. Sanders.

Yet it was the combined strength of Ms. Warren and Mr. Sanders, along with Mr. Biden’s fund-raising and debate difficulties, that frightened moderates enough to lure former Mayor Michael R. Bloomberg of New York and former Gov. Deval Patrick of Massachusetts into the race. Now, though, it’s the left wing of the party that’s growing anxious about how to avoid its own debacle.

A handful of leaders from labor unions have had initial conversations about if, when and how to collectively endorse a candidate and are planning to meet after the holidays, according to a Democrat familiar with the discussions.

Larry Cohen, the former president of the Communications Workers of America, is already thinking well ahead of that. Mr. Cohen supports Mr. Sanders but prefers Ms. Warren stay in the race throughout the primary election to deny a moderate from accumulating a delegate majority. If Mr. Sanders doesn’t win outright, he said, the two senators should demonstrate their combined strength, and amass over half the pledged delegates, so that the left has an upper hand going into next summer’s Democratic convention.

Mr. Cohen, who is concerned that a critical mass of Ms. Warren’s supporters would back somebody else besides Mr. Sanders if she drops out, has been more aggressively making his case to other progressives, including over dinner last week with other Sanders supporters.

But in the near term, he and other left-wing organizers are mostly trying to keep the primary-within-a-primary between Mr. Sanders and Ms. Warren from growing contentious.