Jon Huntsman Jr. sets off Thursday on his first campaign-style swing through New Hampshire, testing whether his moderate brand of politics can find a place in today’s Republican Party.

In a likely presidential bid, he would bring with him a political resume punctuated by his stint as President Obama’s ambassador to China and loaded with centrist positions on immigration, cap-and-trade climate legislation and gay rights.

That could be an uneasy fit in a GOP primary season that is already pushing candidates to the right. So much so that Huntsman’s aides reject the suggestion that he is a moderate — one called it the “M-word” — and describe the former Utah governor as a mainstream conservative with a solid record of antiabortion legislation and tax cuts.

In an up-for-grabs Republican field, Huntsman would enter as a relative newcomer, with a low national profile and a weak presence in the polls. But he couldn’t be dismissed. He is telegenic, has access to a vast family fortune, worked for several presidents and has assembled a team of strategists with national campaign experience — this week he landed a former Mike Huckabee adviser in South Carolina.

Still, Huntsman’s path through the GOP primary would require some airbrushing and some work to build a base of moderate supporters in a party that finds much of its energy and enthusiasm in its conservative wing.

“His strength and his weakness is that he would make a better president than presidential candidate,” said Matthew Burbank, a University of Utah professor of political science who closely watched Huntsman’s tenure as governor. “He was well regarded in Utah, thoughtful, low-key and not prone to scoring political points. And he didn’t always keep the most conservative people happy.”

Huntsman’s path through the primaries would probably be this: Leave the social conservatives to Rick Santorum and Michele Bach­mann, should they run, and instead focus heavily on Chamber of Commerce Republicans, Democrats and independents in the early states with open primaries.

The main obstacle on that route would be Mitt Romney, a longtime Huntsman rival, who has a strong head start in New Hampshire and is eyeing a similar coalition.

Like Romney, Huntsman is a Mormon, but he has something else in common with the former governor of Massachusetts: He must untangle his record from Obama.

“Huntsman’s got to explain” his ambassadorship, said Ed Rollins, who ran Ronald Reagan’s 1984 campaign and advised Huckabee in 2008.

Huntsman has already been offering an explanation that Rol­lins also suggested: “Part of it is ‘I served my country. China was always my area of expertise, and it is an area of critical importance.’ ” Rollins added: “He can try it. It’s not easy, but he can try.”

Rollins said Huntsman could have an easier-than-usual time finessing his past positions, given that the GOP field is full of candidates with similar baggage.

Already, Democrats in South Carolina and New Hampshire are trying to weaken Huntsman — signaling that they see him as a threat — by casting him as an Obama loyalist and a Romney-esque flip-flopper.

At issue is Huntsman’s support for Obama’s economic stimulus package, which he said wasn’t large enough; for the Wall Street bailout; and for cap-and-trade climate legislation, which he has since backed away from, saying recently that it is a flawed approach.

“He’s going to have to answer policy questions, and that’s a bigger challenge, but there is plenty of room in New Hampshire for another candidate,” said Fergus Cullen, former chairman of the Republican Party in the Granite State. “All of the candidates are putting their energy and focus into the so-called tea party activists, and nobody is campaigning for the broad mainstream of primary voters.”

Cullen said that if Huntsman establishes himself as a mainstream conservative, “he will find that there is a significant part of the market open to having a conversation with him.”

Huntsman offers a colorful personal narrative. His family’s fortune was built on fast-food containers. He is a motorcycle-riding former diplomat who once played in a rock-and-roll band called Wizard. Aides say he is a cool version of Romney.

And they point out that Huntsman, who was elected to his first term as governor in 2004, signed flat-tax legislation and three tough antiabortion bills and won plaudits from the National Rifle Association for signing a bill making it easier to carry a concealed weapon.

“Huntsman will appeal to a broad spectrum of voters; he won’t be seen as a right-wing conservative. He is a strong conservative — the M-word doesn’t suit him at all,” said Richard Quinn, a former John McCain presidential campaign aide who is laying the groundwork in South Carolina for a potential Huntsman bid. “He’s not going to be an angry candidate. He’s not one to wave his arms, and his political opponents have liked him.”

Republican strategists say Huntsman could play down Iowa, duel with Romney in New Hampshire, pick up steam in South Carolina — where Romney now trails — and notch a win in Florida, where his campaign would be based, beginning a final march toward the nomination. The Florida-as-centerpiece strategy, however, would have risks, as primary voters and potential donors will want to see an early win as a sign of viability.

So far, Obama’s approach to Huntsman has been similar to his approach to Romney — smothering him with kindness, what aides call an attempt to “hug him to death.”

“As his good friends in China might say, he is truly the yin to my yang. And I’m going to make sure that every primary voter knows it,” Obama joked in a Gridiron Club dinner speech in March. “If you see me on the streets of Nashua, wearing my parka and waving a sign, give me a honk for Huntsman. The next GOP nominee for president. Love that guy.”