Texas Gov. Rick Perry, who skipped New Hampshire to get a head start in South Carolina, said Tuesday's results showed "the race for a conservative alternative to Mitt Romney remains wide open."
"We're nibbling at his heels," Paul said of Romney.
Huntsman had staked his candidacy on a strong showing in New Hampshire, and he announced after the polls closed that he had passed his own test. "Where we stand is a solid position and we go south from here," he said.
Despite struggling to gain 10 percent in New Hampshire, Gingrich and Santorum also said they were in.
About one-third of Republican voters interviewed as they left their polling places said the most important factor in choosing a candidate was finding someone who could defeat Obama in the fall. Romney won their support overwhelmingly.
He ran about even with Huntsman among the one-quarter of the voters who cited experience as the most important factor in selecting a candidate to support.
Paul ran first among voters who cited moral character or true conservatism.
As was the case last week in Iowa, the economy was the issue that mattered most to voters, 61 percent of those surveyed. Another 24 percent cited record federal deficits.
Romney carried the first group and split the second with Paul.
The survey results came from interviews conducted for The Associated Press and the television networks with 2,670 voters across the state. It had a margin of sampling error of plus or minus 3 percentage points.
New Hampshire has a rich history of humbling favorites, front-runners and even an occasional incumbent.
The state's Republican voters embarrassed President George H.W. Bush in 1992, when he won but was held to 53 percent of the vote against Pat Buchanan, running as an insurgent in difficult economic times. Buchanan, who never held public office, won the primary four years later over Sen. Bob Dole of Kansas, who was the nominee in the fall.
In 2000, national front-runner George W. Bush rolled into the state after a convincing first-place finish in Iowa but wound up a distant second behind McCain. Bush later won the GOP nomination and then the presidency.
Twelve Republican National Convention delegates were at stake on Tuesday, out of 1,144 needed to win the nomination.
Obama was unopposed in the Democratic primary.
In his first presidential run in 2008, Romney finished second in the state to McCain. This time, he campaigned with the Arizona senator's endorsement, as well as backing from Sen. Kelly Ayotte and numerous other members of the state's Republican establishment.
Romney committed a pair of unforced errors in the campaign's final 48 hours, and the other contenders sought to capitalize.
On Sunday, after a pair of weekend debates only 12 hours apart, the millionaire former businessman said he understood the fear of being laid off. "There were a couple of times when I was worried I was going to get pink-slipped," he said, although neither he nor his aides offered specifics.
And on Monday, in an appearance before the Nashua Chamber of Commerce, Romney was discussing health insurance coverage when he said, "I like being able to fire people who provide services to me. If someone doesn't give me the good service I need, I'm going to go get somebody else to provide that service to me."
Huntsman, a former Utah governor, saw an opening. "Gov. Romney enjoys firing people. I enjoy creating jobs," he said.
And Gingrich said Bain Capital, the venture capital firm Romney once headed, "apparently looted the companies, left people totally unemployed and walked off with millions of dollars."
Romney has made his business experience a cornerstone of his presidential campaign, saying that Bain on balance created 100,000 jobs, and as a result, he understands how to help boost employment.
He sought to shrug off the attacks, saying he had expected them from Obama in the fall, but Gingrich and others had decided to go first. "Things can always be taken out of context," he said.
Associated Press writers Philip Elliott, Shannon McCaffrey, Kasie Hunt, Beth Fouhy and Holly Ramer in New Hampshire, Brian Bakst in South Carolina and Connie Cass in Washington contributed to this report. Espo reported from Washington.
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