For some voters, Mr. Biden appeals because there are strategic assumptions at work: many black working-class Democrats believe that white America will only support a well-known white male, such as Mr. Biden, while a number of working-class white Democrats also believe he is the most acceptable nominee. Some voters cited the misogyny and racism that female candidates and candidates of color have experienced in previous races.

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And then there is the crucial fact that many of these voters — whether because of his down-to-earth persona, the tragedies he has endured or a combination of both — simply have warm feelings for the man they often address as Joe when they see him.

“He relates well to blue-collar voters and to non-college voters,” Jeff Link, a veteran Iowa Democratic strategist, said. “Those Scranton roots kind of come through.”

Despite this advantage, some Democrats are skeptical that Mr. Biden, who turns 77 on Wednesday, can sustain this support.

Since he entered the race in April, Mr. Biden’s poll numbers have dipped, he has suffered from a series of self-inflicted errors that raised concerns about his age, and he has absorbed ferocious attacks from Democrats and Republicans alike — including baseless attacks on his family from Mr. Trump.

Ty Livesay, the operations manager at a mall in Conway, S.C., said he connected with Mr. Biden — “I’m a common Joe, he’s a common Joe” — but acknowledged having doubts about Mr. Biden’s strength in the primary. “Is Joe going to be able to handle it?” he asked.

Others harbor no such reservations.

“I don’t care about his personal opinion, gaffes or comments he makes — what means most to me is what type of man he is,” said Pete Garrett, who works at an auto parts production company and wore an Obama campaign pin to a Biden appearance in Birmingham, Ala.