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Mr. Huntsman said his third-place finish would allow him to carry on.

“I think we’re in the hunt,” Mr. Huntsman said. “I’d say third place is a ticket to ride. Hello, South Carolina!”

The election results provided disappointing showings for both Mr. Gingrich and Mr. Santorum, who argued that they were the true conservatives in the field. Mr. Gingrich was running a close race for fourth at 10 percent with Mr. Santorum, who failed to capitalize on the momentum from his second-place finish in Iowa, where he lost to Mr. Romney by only eight votes.

“We knew it would be tough,” Mr. Santorum said. “We are going to go on to South Carolina. We have an opportunity to be the true conservative. We can win this race.”

Mr. Gingrich said he, too, would continue to campaign.

“It is doable,” Mr. Gingrich told supporters. “It is a daunting challenge. I will do everything I can to win the opportunity to represent you this fall.”

Early exit polls showed that 60 percent of the voters in the GOP primary described themselves as moderate or liberal on social issues. In Iowa, by contrast, nearly half of all caucus-goers described themselves as “very conservative.”

Mr. Romney, who governed in neighboring Massachusetts, triumphed in his political backyard in spite of increasingly harsh attacks in the final days of the New Hampshire contest, especially by Mr. Gingrich and Mr. Perry, who accused him of “looting” companies and leaving behind broken families as CEO of Bain Capital, a private equity firm. Mr. Romney added fuel to the debate Monday when, advocating for the ability of people to switch health insurers, he said, “I like being able to fire people who provide services to me.”

The sniping pained many conservatives, who worried that GOP candidates were attacking free-market capitalism and giving Democrats valuable ammunition. Conservative talk-show host Rush Limbaugh criticized Mr. Gingrich on his radio program, saying, “This is not the kind of stuff you want said by Republicans. I mean, even the establishment Republicans don’t go after conservatives this way.”

Mr. Romney’s GOP rivals also challenged his record as governor of Massachusetts, arguing that his support of a state-based universal health care program, gun control and tax increases belied his claim to be a conservative.

On the Democratic ballot in New Hampshire, President Obama had no serious opposition, but did run a full-page ad in the state’s largest newspaper touting his 2012 re-election bid.

Mr. Romney now rides the momentum of two consecutive victories into South Carolina’s primary on Jan. 21, where he faces a tougher slog. A group supporting Mr. Gingrich will begin airing ads there Wednesday blasting Mr. Romney as a corporate raider “playing the system for a quick buck.”

As the second-tier candidates battled for second place in New Hampshire, Mr. Gingrich also took a swipe at Mr. Santorum for his 2006 loss in a Senate race to Democrat Robert P. Casey Jr.

“In a sense if there is a clear distinction with Santorum it is that I actually know how to build a nationwide campaign,” Mr. Gingrich said. “He lost Pennsylvania by the largest margin in the history of the state.”

At the Webster Elementary School polling place in Manchester, a massive media horde engulfed Mr. Huntsman as he arrived with his wife around noon. Police, including two atop black horses, worked to control the situation.

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