“I’m surprised he hasn’t been in the middle of it more,” said Tim Miller, a longtime Republican strategist and a “Never Trumper.” “He’s skillfully avoided, to a certain degree, the amount of association he should have with Trump.”

But Mr. Miller said the backlash to Mr. Biden’s comment also “reinforces what a lot of Republicans would say, which is the fact that no matter who the Republican nominee or president or vice president would be, the Democrats would demagogue him.”

Hilary Rosen, a Democratic political strategist, said that Mr. Pence is a smaller target than Mr. Trump, but his conservative politics present a punch list for liberal voters.

“The issues Pence is most identified with,” Ms. Rosen said, “are ones that a majority of voters, including independents, strongly support. So he will be vulnerable.”