In a year when most Republican rivals have vied to match front-runner Donald Trump’s often outrageous proposals, highly personalized attacks and establishment bashing, Ohio Gov. John Kasich stands out as a voice of moderation and compromise.

“Anybody can come around and make a promise: we’re going to do this, we’re going to do that, we’re going to have a 10 percent flat tax, we’re going to abolish the IRS,” Kasich told several dozen people who attended his 87th town meeting Monday.

“That’s not going to happen,” he continued. “So I’m here giving you what I would need to do to govern, not to get elected.” And he asked, “You don’t think we can solve these problems without both parties, do you?”

But Florida Sen. Marco Rubio’s close third in Monday’s Iowa caucuses threatens Kasich’s hope of emerging as the top establishment candidate in next Tuesday’s New Hampshire primary.

He professes to be unconcerned, telling a Bloomberg Politics Breakfast Briefing Wednesday, “The media is going to pump this for a couple days and ... then we’re going to see.”

Later, at the governor’s 93rd town meeting in Newmarket, two likely Kasich voters dismissed the Iowa impact here. “He didn’t make much effort there, so I discount it,” said Bill Healey, 78, a retired computer systems consultant.

“Iowa is Iowa,” said his wife, Crescentia Anne Healy, 79. “We’re so different.”

Kasich’s campaign, which stresses his conservative credentials in balancing the federal budget in Congress and governing Ohio the past six years, isn’t totally positive. On Monday, he condemned “negative crap” in the advertising of rivals Chris Christie and Jeb Bush. That night, his independent Super PAC, New Day for America, aired a television ad showing Bush encased in mud.

But the approach enabled Kasich to rise in mid-January to second in the Real Clear Politics average of New Hampshire polls and he leaves many undecided voters with positive vibes.

Most New Hampshire newspapers have endorsed him, as have The Boston Globe and The New York Times, which called Kasich “the only plausible choice for Republicans tired of the extremism and inexperience on display in this race.”

But Rubio’s strong Iowa showing has complicated Kasich’s effort to beat the Florida senator, along with Bush and Christie. “They all have to beat each other to have an opportunity to consolidate mainstream voters and donors,” said Fergus Cullen, a former state GOP chairman who backs Kasich.

However, even some past candidates who made unexpectedly strong showings in New Hampshire — Democrat Gary Hart in 1984 and Republican John McCain in 2000 — failed to sustain their momentum afterwards.

“What we have to do is get to March 15,” said veteran New Hampshire pol Tom Rath. That’s when the primary calendar moves to Kasich’s home state of Ohio and other Midwestern bastions, and when winning candidates can win all of a state’s delegates rather than dividing them proportionally.

That not only requires finishing second here, it means doing well in Massachusetts and Vermont and surviving primaries in conservative strongholds like South Carolina on Feb. 20, and Texas on March 1.

Still, even before Iowa voted one veteran Washington analyst, Stuart Rothenberg, wrote in Roll Call that, even if Kasich beats Rubio here, “the Ohio governor simply has not shown the appeal — or put together the campaign elsewhere — that he would need to become a true contender in the Republican race.

“If I get smoked here,” Kasich said in Newmarket, “I’m going (back) to Ohio.”

He added he is also “prepared to move forward. But it’s in the hands of the people of New Hampshire.”

Carl P. Leubsdorf is the former Washington bureau chief of the Dallas Morning News.