“He’s a bright guy. He’s intelligent. He’s been through this many, many times. And he’s what is referred to in Yiddish as a ‘mensch,’” said Mr. Bergstein, 70, who is backing Mr. Biden. “Unfortunately, his opponent doesn’t have that skill.”

Still, Mr. Bergstein expressed some concerns about how others might perceive the president’s age.

“The only thing I worry about is sometimes I think people don’t listen and they just look. So Biden’s, you know, 80 whatever years old and he doesn’t run. He walks,” he said. “You know, so do I sometimes.”

Mr. Trump has also spent months mocking Mr. Biden as a weak and incompetent debater. In May, he called Mr. Biden “the WORST debater I have ever faced. He can’t put two sentences together!”

But in recent days, he has sought to reset some of those expectations. Last week, he called Mr. Biden a “worthy debater,” praising Mr. Biden’s performance in vice-presidential debates against Paul Ryan in 2012.

Samuel Palmer, a retiree from Nampa, Idaho, said he expected Mr. Trump to be “extremely well prepared” for the debate. But he worries about the format, which includes no audience and a rule that each candidate’s microphone will be muted when it is not their turn to speak. In recent days, the Trump campaign has attacked the debate moderators, two veteran CNN journalists, by accusing them of biased coverage of Mr. Trump in the past.

“With the debate moderators having such control over, you know, how this whole thing is going to be going, I think that puts him at a little bit of a disadvantage to a certain extent,” said Mr. Palmer, 68, who is supporting Mr. Trump. “But he’s more than capable of putting on what I would hope to be an extremely well done and factual performance.”

Camille Baker contributed reporting.