HAMPSTEAD, N.H. — Hours after landing what was arguably his strongest moment of any recent debate, Jon Huntsman refueled his attack on Mitt Romney, who had questioned how an aspiring conservative could serve a Democratic president.

“Apparently Mitt Romney doesn’t believe in putting your country first,” Huntsman said on Sunday, encircled by a hoard of hundreds of New Hampshire locals who were unable to fit inside the coffee shop where Huntsman had just made an appearance.

Huntsman left his post as Utah’s Republican governor when President Obama asked him to serve as U.S. ambassador to China. Romney, who is straining to convince GOP voters he’s a true conservative himself, has used that entry on Huntsman’s résumé to argue that Huntsman is tainted by his service to a president he says has failed.

“He’s got this bumper sticker that says ‘Believe in America,’ ” Huntsman said. “It’s just phony nonsense.”

Huntsman scored major points earlier Sunday during a Facebook/NBC News debate when he pledged to always put his country first and said attitudes like Romney’s reveal why the nation is so divided.

But sitting just under the surface of Huntsman’s retort is another, more nuanced argument: that come time for the general election, Huntsman is the candidate with the potential for crossover support that Republicans will need if they seek to take back the White House.

Asked whether he would win Tuesday’s primary in New Hampshire, where Romney has long dominated the Republican field, Huntsman did little to temper expectations.

“It’s sure feeling like it,” Huntsman said, flanked by a gaggle of reporters and voters 10-deep, who moved with him like a herd as he progressed to his car.

The car started moving — with Huntsman behind the wheel — but the candidate didn’t stop talking. As he inched through the parking lot, Huntsman worked the crowd like a vehicular rope-line, answering questions through an open driver’s-side window.

“We've gone from margin of error, the very back of the pack, to right near the top,” Huntsman said, one hand on the wheel. “It’s changing hour by hour.”

And he’s right. Polling suggests Huntsman is gaining ground in New Hampshire, where he needs at least a top-three finish to stay alive in the fight for the GOP nomination.

Daily tracking from Suffolk University on Sunday showed Huntsman has pulled into third place, with 11 percent. And Public Policy Polling, a Democratic firm that will release a new survey of New Hampshire voters later Sunday, said the margin is narrow between Huntsman and Ron Paul, who is currently occupying the No. 2 slot. The firm said Huntsman could plausibly eke out a second-place finish in New Hampshire on Tuesday.