NEW YORK — Donald Trump’s campaign on Wednesday hailed Mike Pence’s debate performance as proof of Trump’s readiness for the presidency, trumpeting Trump’s judgment in picking a seasoned running mate as Democrats ridiculed Pence for failing to defend Trump’s ideas and policies.

Kellyanne Conway, Trump’s campaign manager, argued on several television programs that Pence, the governor of Indiana, had vindicated the man at the top of the Republican ticket during his Tuesday night clash with Senator Tim Kaine of Virginia.

Kaine mounted an insistent and prodding attack on Trump and Pence at the 90-minute debate, frequently interrupting Pence to demand that he defend Trump’s politically divisive statements.

An unruffled Pence sidestepped those demands, repeatedly asserting that Trump had not said things that he actually did say, and delivering something close to a boilerplate Republican message attacking taxes and business regulation.

Pence took something of a victory lap in Harrisonburg, Va., where Ed Gillespie, a former chairman of the Republican National Committee, introduced him as “one heck of a debater.’’

Pence said Trump had called the night a win for the top of the ticket.

“From where I sat, Donald Trump won the debate,’’ Pence said. “Donald Trump’s vision to make America great again won the debate.’’ He repeated his charge, from the debate, that Kaine and Hillary Clinton have been throwing “an avalanche of insults’’ in the campaign.

Trump’s temperament and readiness for the presidency have emerged as central concerns for voters, so the hope among Trump allies is that Pence may have reassured Americans that Trump is calm enough for the job.

Conway said on Fox News that Pence highlighted “the great judgment and leadership’’ that Trump has exercised in choosing a running mate.

Democrats dismissed that notion Wednesday. Acknowledging that Pence had been a more placid performer than Kaine, they countered that Kaine had successfully trained his fire on Trump, the defining figure in the race, and exposed Pence as incapable of defending Trump on the merits.

In Ohio, Bill Clinton chuckled and described Pence as having tried to “shimmy out of a discussion’’ on basic economic issues like the minimum wage and equal pay for women.

And Democrats assailed Pence for having misrepresented the positions and past comments of Trump; the Clinton campaign released a video showing Pence’s denials alongside clips of Trump’s remarks. The video concludes with a dig at both Pence and Trump: “It’s OK, Mike. We’d have a hard time defending him, too.’’

John Podesta, chairman of Hillary Clinton’s campaign, said on MSNBC that Pence had been “smooth,’’ but ineffective. Kaine’s goal, Podesta said, was to “challenge Mike Pence to defend Donald Trump, and Mike Pence didn’t do it.’’ Podesta suggested Pence might be more interested in protecting his own political future than winning the current election.

There is scant polling information on how most voters reacted to the debate, and it is unclear that an encounter between comparatively low-key running mates might reshape a race waged between two outsize presidential candidates.

A snap poll conducted by CNN found that Pence was seen as the victor by a small margin, with 48 percent of respondents calling him the winner and 42 percent naming Kaine.

But any shift in state and national polls after the vice presidential debate might not show up before the next debate between Trump and Clinton, on Sunday — a far more consequential event in the race, and one that is much likelier to shift voter attitudes.

Conway expressed confidence Wednesday that Trump would offer a “powerful performance’’ in the second presidential debate, a town hall-style discussion at Washington University in St. Louis.

Trump is seen as needing a recovery in the second debate after a dismal performance against Clinton Sept. 26. He has slipped markedly in the polls.

And he has faced mounting questions about his treatment of women and the possibility that he may not have paid federal income taxes — two subjects that Pence avoided discussing at length on Tuesday.