Yet the reluctance of Democratic lawmakers to embrace Ms. Warren’s campaign this deep into the year, after she has plainly emerged as a leading candidate, illustrates both the lingering reservations party elites have about her general election prospects and her unique positioning in this race.

“Racing to the left is not really speaking to the needs of people in the heartland,” said Chicago Mayor Lori Lightfoot, who expressed alarm about scrapping private health insurance, urged the candidates to focus on “pocketbook issues” and, when asked if Ms. Warren could reclaim the Midwestern states Mr. Trump captured in 2016, paused before saying: “I’m not sure.”

Ms. Warren is politically neither fish nor fowl.

She is not an anti-establishment insurgent in the style of Mr. Sanders, who were he in the position Ms. Warren is now would almost certainly have inspired a Stop Bernie campaign funded by a petrified donor class. But with her refusal to raise money among rich contributors, her unabashed populism and her pre-Senate roots in academia, she is hardly a Clinton-style creature of the Democratic political class.

As a result, many party officials are neither rushing to oppose her nor racing to her side, instead staying on the sidelines and doing what politicians often do when they are uncertain of what choice to make: buying time.

“It’s easier to wait, you keep your relationships good,” said Representative Deb Haaland of New Mexico, one of the few lawmakers who is supporting Ms. Warren, noting that some of her colleagues are loath to offend their friends in the race by choosing a candidate.

Reinforcing this instinct toward caution is the fluid nature of a primary still large enough to feature 12 candidates on the debate stage this week as well as the high stakes of next year’s general election.

“You had two candidates last time,” said longtime Representative Rosa DeLauro of Connecticut, referring to the Sanders-versus-Hillary Clinton race. “People want to see this unfold.”