Joyce Brodsky, a retired art teacher in Kewadin, Mich., noting how Mr. Biden and his wife, Jill, extended sympathy to the Trumps, said she was unable to feel so selfless.

“I’m more of a ‘serves you right’ type of person,’’ she said.

While some Biden supporters spoke of the president’s illness as payback — for holding rallies, mocking Mr. Biden for wearing masks, generally refusing to wear a mask himself — Cliff Canaan, in Philadelphia, had only one comeuppance in mind: being able to vote Mr. Trump out on Nov. 3.

“I think it’s very important that the people have their say in rejecting what he stands for,’’ said Mr. Canaan, 31, a software manager for a bank. “I don’t want him to resign or be out of office in any other way than by the ballot box.”