Elizabeth Bowens, a retired hospitality worker in Myrtle Beach, S.C., said that she disliked the contentious tone of the Democratic race and that she longed for the Obama years. “Him and Michelle, that’s a beautiful couple,” she said.
But Ms. Bowens did not seem to be leaning toward Mr. Biden.
“It’s time for a woman,” she said.
To Mr. Obama’s sharpest critics on the left — chiefly activists and policy experts concerned with issues like financial regulation, drone warfare, immigration and criminal justice — his Teflon reputation can be frustrating.
Matt Stoller, a fellow at the liberal Open Markets Institute who is a scathing critic of Mr. Obama’s economic record, said he saw Democrats as caught between their personal reverence for Mr. Obama and the reality that the country faces “existential crises” — on matters like climate change and economic inequality — that Mr. Obama did not resolve.
At some point, Mr. Stoller said, Democrats might face a stark choice between Mr. Obama’s center-left policy framework and the agendas of liberal candidates they now favor. But Mr. Stoller acknowledged no such test had yet arrived.
“I’m still waiting for that moment when Democrats are going to have to make that choice,” he said.
There is no guarantee that it will ever arrive. And the choice Democratic primary voters see before them now has less to do with Mr. Obama’s policies than with the immediate challenge of ousting President Trump.
Susan Chase, a retiree in Southport, N.C., said candidates who attacked Mr. Obama would not get her vote, and she criticized Senator Kamala Harris for attacking Mr. Biden in the first debate.
But that does not mean she will vote for Mr. Biden.
“Part of me says it’s time for something really new and different,” Ms. Chase said, “but then the other part says we’ve got to have somebody who can beat Trump.”
Jonathan Martin contributed from Galivants Ferry, S.C., Katie Glueck from Birmingham and Reid J. Epstein from Washington.