Ahead of what is being billed as a make-or-break event, the Hillary Clinton and Donald Trump camps are each boasting about how the town-hall style format of the second debate this weekend plays to its candidate’s strengths, raising the stakes for the high-profile showdown.

The declarations of confidence have cut against traditional conventional wisdom that says candidates are better off lowering expectations than raising them, just in case they flop.

The dynamic is adding to the intrigue into the face-off Sunday in St. Louis, where Mr. Trump hopes his interactions with undecided voters will help him recapture the momentum that he lost after the first debate last week.

The New York businessman has done more to prepare this go-round, and on Thursday he held an invite-only town hall in Sandown, New Hampshire — marking a break from his usual rallies and a chance for him to do a dry run in a setting somewhat similar to the one he will find himself for 90 minutes Sunday.

Mr. Trump, though, shook his head in disbelief at the idea that he was there for some sort of debate preparation, and the event, where he fielded questions that came from supporters, reflected his point.

“They were saying this is practice for Sunday. This isn’t practice, this has nothing to do with Sunday,” Mr. Trump said, standing steps away from a two-minute clock that was meant to time his answers. “We are just here because we just wanted to be here. And you know Hillary, frankly, they talk about debate prep. It is not debate prep, she is resting, she’s resting, and I want to be with the American people.”

“You really think Hillary Clinton is debate prepping for three or four days?” he said, returning to the subject. “She is resting, she wants to build up her energy for Sunday night.”

Mrs. Clinton, who is very experienced in the town-hall setting, was holed up in Washington gearing up for the second showdown, and allowed her army of surrogates to do the talking for her at various campaign events around the country.

“We are very enthusiastic about this debate format,” Clinton campaign manager Robby Mook told reporters in a conference call. “We think that it is going to be a fantastic opportunity for Secretary Clinton to connect with voters and really be able to explain in detail the plans she has to improve their lives.”

Trump campaign manager Kellyanne Conway said Mr. Trump has reviewed the footage from the first debate and plans will be ready.

“Well he learned from those tapes that he was trying to answer the questions as they were asked,” Ms. Conway said on ABC’s “Good Morning America.” “Mrs. Clinton was there really trying to get out the five or six zingers she had rehearsed for a number of days. So this time, I think that Donald Trump, in a town hall format, it’s one he’s very comfortable.”

The pro-Trump and pro-Clinton forces, meanwhile, are blasting out cherry-picked data from early voting and registration efforts that boost their claims that their candidate is best positioned them to win an election that both sides agree could break voter turnout records.

Mr. Mook said there have been “excellent turnout numbers” among women, Hispanics and Asian-Americans — suggesting that bodes well for Mrs. Clinton, who is banking on strong support from minorities.

“We think that is in large part due to the hateful and divisive rhetoric that we are seeing from Donald Trump and his campaign,” Mr. Mook said.

The Republican National Committee is putting a different spin on the numbers, arguing they have been registering voters at a faster clip than Democrats in key swing states like Florida.

“We are seeing positive trends really across the board,” Chris Carr, political director for the RNC, said Thursday.