In phone interviews, dozens of Democrats, mostly aged 50 and over, who live in key March primary states like Massachusetts, Virginia, Michigan and Florida, said that Mr. Biden’s appeal went beyond his case for how to beat President Trump. It was his chances of overtaking Mr. Sanders, the only candidate in the vast Democratic field they found objectionable for reasons personal and political.

For some, like Amy Siegel of Natick, Mass., the anti-Sanders feeling relates back to the 2016 Democratic primary, when she supported Hillary Clinton and believed Mr. Sanders ran a divisive campaign that wounded her ahead of the general election. This time around, Ms. Siegel, 57, initially supported Mr. Buttigieg. But she voted for Mr. Biden in her state’s primary, held on Super Tuesday, days after Mr. Buttigieg dropped out and endorsed the former vice president. Ms. Siegel said she decided to flip her vote even before Mr. Buttigieg exited the race.

Others, like Beatrice Abetti of Bonita Springs, Fla., switched to Mr. Biden after Ms. Warren suspended her campaign, viewing Mr. Sanders as a general election risk. Ms. Abetti, a 69-year-old author and former professor, said centrist Republicans she thought were critical to an Electoral College victory saw Mr. Sanders as a fringe leftist, even if she supported his policies.

“I can wait for four more years for ‘Medicare for all’ and the Green New Deal — and go with Biden — just to get Trump out of office,” Ms. Abetti said, “because that’s my number one thing.”