Republican presidential candidate John Kasich exits his bus outside a VFW post in Raymond, N.H, on Wednesday. The town hall was Kasich's 94th New Hampshire event. (John Tully for the Washington Post)

John Kasich arrives at campaign events with a large electronic sign that ticks off the increasing national debt in milliseconds.

He does not care for the overtly religious tone of some of his Republican presidential rivals, saying that he does not want to combine God and politics, because “I’m not comfortable doing it.”

And while most of his rivals hurl insults at one another, Kasich repeatedly refuses to directly attack.

In a GOP presidential campaign dominated by anger over illegal immigration, distrust of establishment leaders, and aggressive courtship of evangelicals, the Ohio governor is trying to turn Tuesday’s New Hampshire primary into a test of whether his party has room for a throwback brand of Republicanism.

More than any of his GOP rivals, Kasich has bet everything on a strong finish here. He opted not to compete in the Iowa caucuses, which were heavily influenced by religious conservatives, and tells New Hampshire voters that he will drop out if he does poorly here.

John Kasich, who has bet everything on Tuesday’s primary in New Hampshire, addresses voters at an event at the Raymond VFW post. (John Tully for the Washington Post)

As he travels the state, Kasich is emphasizing fiscal policy and other issues that have long been important to Republicans but have not animated the party base in recent elections.

He boasts his centrist credentials, embracing his decision in Ohio to accept more Medicaid funds as part of President Obama’s health-care law.

“I guess sometimes when you talk about caring for people, sometimes it is not a tone we’ve heard in the Republican Party for quite a while,” he said in an interview with The Washington Post on his campaign bus.

Kasich’s approach is an echo of what George W. Bush once called “compassionate conservatism,” with the Ohio governor arguing that the party cannot foment only anger and resentment.

The governor’s style was apparent this week during an appearance at a VFW hall, when a questioner all but invited him to attack Donald Trump by inquiring about the Republican presidential front-runner’s treatment of people with disabilities.

Kasich declined the opportunity. Then Kasich choked up, on the verge of tears. He motioned for the questioner to stand, reaching out his arms and embracing her in an unexpected hug. He struggled to regain his voice.

The battle continues in New Hampshire as candidates fight tooth and nail to take home the state. The Post’s David Weigel walks through what it will take to win the New Hampshire primary. (Dalton Bennett/The Washington Post)

Asked later what prompted his emotional moment, Kasich said he was thinking about children with disabilities who need extra care, an issue he said he has seen firsthand many times as governor.

“It’s easy to run over the weak,” he said at a town-hall meeting in Durham. “I’m not going to do it.”

Kasich is convinced that he has struck political gold by carving out a niche in the crowded GOP field. Trump has drawn large crowds to his rallies, bashing rivals. Sen. Ted Cruz (R-Tex.) is seeking to capitalize on his Iowa caucus victory, leaning heavily on evangelical support. Sen. Marco Rubio (R-Fla.), former Florida governor Jeb Bush and New Jersey Gov. Chris Christie are fighting for the GOP establishment vote.

Kasich likes to say he is in his “own lane.” Asked in the interview what that means, he said he is an “inside-outside” player. Although Kasich has been a House Budget Committee chairman and is a governor, he said in the interview that “I’ve never been in the establishment. I’m not anti-establishment, but I can work with the establishment.” He boasts of collaborating with liberal Democrats to pass legislation. He says he believes humans contribute to global warming. He is in favor of government support for those with disabilities.

Kasich summed up his view this way: “It is a twist and turn and a different definition of what is conservative and what it means to be a Republican.”

He boasts of endorsements from the Boston Globe, the New York Times and a number of New Hampshire newspapers, rejecting suggestions that support from left-leaning and moderate editorialists could backfire. He cites polls that show him in second place, or statistically tied for that standing, behind Trump.

An average of recent New Hampshire polls, as analyzed by The Post, found that Trump leads with 35 percent, followed by three candidates who are statistically tied because of the margin of error: Cruz at 12 percent, Rubio at 11 percent and Kasich with 10 percent.

As he travels the state, Kasich shows allegiance to a classic New Hampshire strategy of interacting with smaller audiences. His stop at the VFW post on Wednesday was his 94th town-hall meeting in the state.

He is a happy wonk on the hustings, traveling with a handful of aides in a campaign bus fit for a rock star and stocked with plenty of snacks. Wearing a Kasich-themed fleece, he walks up to voters like a talk-show host and leans close to them when they ask questions. He veers between preachiness and corny jokes.

Wherever he goes, Kasich often seems to feel as though he is being goaded into attacking his opponents.

At a Wednesday breakfast with reporters, he was given the perfect opportunity to “win the morning,” as the saying goes. Television cameras rolled at an event sponsored by Bloomberg Politics as he was pressed to go after his opponents. Reporters pounced when he said that “I don’t go out and try to win a vote by using God. I think that cheapens God.” Whom was he talking about? He wouldn’t say.

“Why don’t you figure it out?” Kasich responded. “You’re a smart guy.”

Did he agree with Christie’s assessment of Rubio as being a boy in a bubble?

“Pass.”

Still, Kasich sometimes does try to have it both ways. He lamented that a “dark and negative message is coming from Cruz and Trump. You figure it out. I’m not here to attack other candidates today. I’m sorry; I’m just not doing it.”

Never mind that it sounds as though he may have done just that by casting his opponents as being on the dark side. Moreover, a pro-Kasich super PAC, New Day for America, has attacked opponents such as Trump. That prompted rare attention from the real estate mogul, who tweeted, “I want to do negative ads on John Kasich, but he is so irrelevant to the race that I don’t want to waste my money.”

Kasich, who doesn’t control the super PAC, insists that he is walking on the “sunny side,” declaring that “I’m not all that doctrinaire.”

Interviews with voters at his events found that many are drawn to him by the perception that he is a moderate. Fred Hochgraf, 83, a retiree from Durham, described himself as a moderate “Rockefeller Republican” but said the party had walked away from him long ago. “This is the first breath of fresh air I’ve had,” he said after listening to Kasich. Similarly, Darlene Graczyk, a retiree from Atkinson, said she is “definitely moderate” and is considering voting for Kasich.

Kasich is betting his campaign on a strong showing in New Hampshire, which has a much smaller percentage of evangelicals than Iowa does and has a history supporting independent-minded candidates.

If he is “trounced” here, Kasich said in the interview, he will head with no regrets back to Ohio, where he does, after all, have a job as governor and a family that includes 16-year-old twin daughters. So, he is asked, what is the definition of trounced?

“We’ll all know if I’m trounced,” he said. “It’s at the bottom.”