Indeed, since his selection as a running mate, much of Mr. Pence’s job has been to help explain or clean up Mr. Trump’s persona. Yet he has distanced himself in some important instances, including suggesting humans play a role in climate change — an acknowledgment on the part of his aides that a political future inextricably tied to Mr. Trump could be perilous.

Mr. Pence already has experience defending his running mate on the Sunday news shows and in other television interviews, which aides say has also helped prepare him for the debate.

“Ultimately, he’s going to have to explain Trump to people, and his job is probably going to be to mop up whatever mistakes Trump makes and explain Trump and be the guy who says, ‘Trump’s a good guy and he’s not crazy,’” said John Feehery, a Republican strategist who is not working for the campaign.

But, Mr. Feehery added, though Mr. Pence has revealed himself as a loyal soldier, he is also likely to display at least some instinct of self-preservation. “Part of it is to explain Trump but don’t necessarily fall on your sword for him,” he said.

To that end, Mr. Kaine’s task is more straightforward.

Mr. Kaine has already faced some tough questions about Hillary Clinton, the Democratic presidential nominee, on subjects like her use of a private email server and her trustworthiness. But he has not been forced to play cleanup the way Mr. Pence has.

On the campaign trail, Mr. Kaine cheerfully talks up Mrs. Clinton’s agenda while building a thorough case against Mr. Trump on a variety of subjects, from his refusal to release his tax returns to his views on foreign affairs. The debate offers a platform to do the same thing — just on a much bigger and more pressure-filled stage.

“It is going to be easier for him than it is for Mike Pence,” said Mo Elleithee, who advised Mr. Kaine when he ran for governor and senator and also worked on Mrs. Clinton’s 2008 presidential bid. “Kaine genuinely, I think, shares Hillary Clinton’s worldview.”

“I would expect Kaine is going to be hitting a lot of the same themes that Hillary Clinton hit in the last debate,” added Mr. Elleithee, who is now the executive director of Georgetown University’s Institute of Politics and Public Service.

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Senator Tim Kaine last month in Ann Arbor, Mich. A Democratic strategist said it would be easier for Mr. Kaine than for Mr. Pence because he is more closely aligned with his running mate, Hillary Clinton. Credit Paul Sancya/Associated Press

Mr. Kaine has prepared to fend off what his advisers expect will be aggressive attacks by Mr. Pence aimed at Mrs. Clinton, according to campaign aides. And his team is wondering how far Mr. Pence will go in defending Mr. Trump.

Mr. Kaine does not devote much time to talking about Mr. Pence when he campaigns, and his focus on the top of the ticket is not likely to change on Tuesday night.

“It really is more about Donald Trump than it is about Governor Pence,” Mr. Kaine told reporters on his campaign plane recently, discussing the vice-presidential debate.

Similarly, Mr. Kaine is set to promote what a Clinton presidency would look like. “If I talk too much about Tim Kaine during my debate,” he said, “I’m wasting my time.”

If Mr. Trump’s debate preparation so far has largely resembled his campaign — haphazard and unfocused — Mr. Pence’s reflects his sharply different approach: methodical, disciplined and systematic.

He and his team began preparing for the debate shortly before Labor Day, and each week have devoted an increasing amount of time to the effort. (Fridays, which Mr. Pence typically spends off the trail and in the Indiana governor’s mansion, have become largely focused on debate preparation.)

He has been studying briefing books, and dossiers on his laptop. The Republican National Committee has also uploaded copious videos of Mr. Kaine — everything from interviews to past debates — to an online file-sharing service for Mr. Pence to view.

The Clinton team has revealed little about Mr. Kaine’s preparations, though Mr. Kaine talked a few weeks ago about reading “endless debate prep memos,” a subject that he said Mrs. Clinton had joked to him about. “She said, ‘You know, our staffs know how to kill a lot of trees by putting together massive books,’” he said.

In Mr. Kaine’s mock debate sessions, Mr. Pence is being played by Robert B. Barnett, a Washington lawyer who has long served as a faux adversary in debate preparations for presidential and vice-presidential candidates. Earlier in the campaign, he played Senator Bernie Sanders when Mrs. Clinton practiced to debate him.

Jerry Kilgore, a Republican who ran against Mr. Kaine for governor in 2005, said he found debating Mr. Kaine a frustrating experience.

“He’s absolutely going to come off as believable with everything he says,” Mr. Kilgore said. “He says everything with such sincerity.” He added that Mr. Kaine came across that way whether or not Mr. Kaine was being completely forthright.

“That’s the danger Governor Pence has in this debate,” said Mr. Kilgore, a former Virginia attorney general.

When Mr. Pence accepted the No. 2 slot, he and his team outlined three milestones they believed would require flawless execution: his initial rollout, his convention speech and the debate. The same close-knit team of advisers who helped plan the first two milestones — Nick Ayers, the chairman of the vice-presidential campaign; Marc Short, a senior adviser; and Josh Pitcock, the campaign’s policy director — have also been handling Mr. Pence’s preparation.

Mr. Pence’s team decided it would be smart for him to attend last Monday’s debate at Hofstra University — not just to cheer on Mr. Trump, but to experience the drama and optics of a presidential debate, without the high-stakes pressure.

The Clinton team took a different approach. Mr. Kaine dropped by a debate watch party in Orlando, Fla., but left before the debate began.

“I wish I could actually hang and watch it with you, but I’m actually doing homework tonight,” he told the crowd. “I have to go sit down and get in the zone and with a yellow pad, you know, take a million notes.”

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