GOP race moves south after Romney wins New Hampshire

• NEW: Mitt Romney says he'll focus on Obama's failures
• Romney sweeps the first two contests of the nominating process
• Ron Paul finishes a solid second, with Jon Huntsman in third
• Romney sounds like the presumptive nominee in his victory speech

Manchester, New Hampshire (CNN) -- Former Massachusetts Gov. Mitt Romney won a convincing victory in the New Hampshire primary, the second straight triumph for Romney and one that bolsters his front-runner status to take on President Barack Obama in November.

All six Republican contenders head to South Carolina on Wednesday ahead of the next primary.

With 95% of precincts reporting, Romney received 40% of the vote in Tuesday's balloting. Texas Rep. Ron Paul received 23% and former Utah Gov. and U.S. Ambassador Jon Huntsman garnered 17%.

Romney's sweep of the first two contests for the GOP nomination made history. It was the first time a non-incumbent Republican won both the Iowa caucuses and New Hampshire's first-in-the-nation primary.

Former House Speaker Newt Gingrich and former Pennsylvania Sen. Rick Santorum came in with 10% and 9%, respectively, and Texas Gov. Rick Perry had 1%.

"We didn't compete in New Hampshire. So it doesn't surprise us that our score there was a bit on the low side," Perry said on "Piers Morgan Tonight."

With Romney's New Hampshire victory expected, based on polling in recent weeks, the battle for second place and beyond had implications for the South Carolina primary on January 21.

Romney leaves N.H. with wind at back

Despite the strong showing by Romney, who won nearly every group of voters after his narrow victory last week in the Iowa caucuses, all the other contenders made clear they would continue their campaigns in South Carolina.

The Palmetto State will be the first Southern contest of the nomination process and more welcoming to conservatives such as Santorum, Perry and Gingrich, who hails from neighboring Georgia.

"South Carolina is a winner-take-all state," Perry said. "Winning here, I can promise you, wipes out the caucus victory and New Hampshire. So if Mitt's thinking he's got it in the bag, I think he'll be in for a great surprise in South Carolina when he shows up here."

In an interview with CNN before Tuesday's results came in, Gingrich acknowledged South Carolina will be vital to his presidential hopes.

"We're going to go all out to win South Carolina. We think that's a key state for us," Gingrich said, describing the race there as a contrast between himself -- a "Georgia Reagan conservative" -- and Romney, "a Massachusetts moderate."

Romney told CNN Wednesday he does not plan to discount the other candidates and noted he has "a long way to go" to secure the GOP nomination.

However, he said, "I really think we're best off focusing on the failures of this president." He said he believes voters want to hear his plans for restoring rising incomes and job growth.

In his victory speech in New Hampshire, Romney sounded like the presumptive Republican nominee to take on Obama in November.

"Tonight we celebrate. Tomorrow we go back to work," Romney told exuberant supporters, calling Obama "a failed president" and asking "the good people of South Carolina to join the good citizens of New Hampshire to make 2012 the year he (Obama) runs out of time."

The crowd interrupted with chants of "Mitt" as he outlined a campaign strategy that portrayed Obama as a European-leaning big government advocate while defining his candidacy as a return to American ideals.

"This president puts his faith in government. We put our faith in the American people," Romney said to cheers.

Paul told CNN that he expected to raise more money after a second-place finish, and he then told cheering supporters that their campaign for freedom in America would continue to grow.

Paul: Only I can stop Romney

Referring to Romney, Paul said "he certainly had a clear-cut victory, but we're nibbling at his heels," giving a chuckle as the crowd chanted "President Paul."

In response to criticism by rivals that his calls for scrapping the Federal Reserve and bringing home American forces from around the world were dangerous, Paul declared: "We are dangerous, to the status quo."

Huntsman told his supporters, "I think we're in the hunt," adding "Hello, South Carolina" to emphasize his third-place finish would keep him in the race.

Huntsman's surge stops at 3rd place

Santorum, who narrowly lost to Romney in Iowa but finished well back in New Hampshire, also said he would head to South Carolina and continued to portray himself as the "true conservative" in the field.

"With faith in American people we can not only wipe out this deficit and rebuild this economy ... but we can win a huge victory that will rally this country to take on the challenges we have before us," Santorum said.

Santorum hits rockier road in N.H.

Perry already was in South Carolina in what amounted to a concession of New Hampshire.

A record 250,000 voters were expected to turn out in New Hampshire for the GOP primary on an unseasonably warm winter day, Deputy Secretary of State David Scanlan told CNN. With no competitive challenger to Obama on the Democratic side, more "undeclared" voters could weigh in on the Republican race, he said.

Exit poll data showed that nearly seven out of 10 Republican voters in the state were very worried about the economy and their personal financial situation.

One in four said the deficit was the most important issue. Also, more than three-quarters of respondents said the series of Republican debates was important to their final decision, while less than half said television ads were important.

The exit poll data showed that Romney scored a solid victory. Even Christian conservatives and tea party backers -- the heart of Santorum's support last week in Iowa when he lost by just eight votes to Romney -- gave a plurality win to Romney this time.

Still, most New Hampshire voters indicated they only made up their minds this week.

One of the state's more than 300,000 "undeclared" or independent voters, Linda Underhill, said Tuesday that she decided to support Huntsman.

After initially backing Romney, Underhill shifted to Huntsman, calling him smart and likely to take a bipartisan approach.

"In the past few days, I watched him very closely," Underhill said. "I just feel he is more genuine."

Earlier Tuesday, Gingrich argued that a Romney showing in the 30% range, as the most recent polling suggested, could hurt the front-runner even if he won Tuesday's contest.

"If he can't come close to 50% here, it's very unlikely he can sweep the nomination," Gingrich told reporters in Bedford. "And I think that gives the party time to take a deep breath, look at his record and begin to realize that maybe this isn't the right guy to run against Obama."

Gingrich has been pounding at Romney since Iowa, complaining about a massive negative ad campaign against him by allies of the former Massachusetts governor.

A Gingrich-allied super PAC has already launched its own anti-Romney barrage in South Carolina, and Gingrich and others have honed in on Romney's years as a financier with Bain Capital, accusing him of getting rich by gutting companies and laying off workers.

Romney will have to answer questions about that in conservative South Carolina, Gingrich said Tuesday.

Asked about the negative ads from the Gingrich camp, Romney told Boston radio station WRKO on Tuesday that they "will not help" his rival.

"All I have got to do is keep my head down, keep talking about my message of getting America back to work, my experience in having led two businesses successfully, the Olympics successfully," Romney said.

Gingrich wasn't alone in attacking Romney's business record. In South Carolina, Perry told supporters Romney's firm "looted" a photo company in Gaffney and a steel company in Georgetown.

"I would suggest they are just vultures," Perry said. "They are vultures that are sitting out there on the tree limb waiting for the company to get sick, then they swoop in, they eat the carcass, they leave with that and they leave the skeleton."

Asked about those remarks on Wednesday, Romney said the issue has been brought up every time he has run for an office.

"I understand that President Obama is going to try and put free enterprise on trial," he said. "But, you know, Rick Perry and Newt Gingrich are going to be the witnesses for the prosecution. I'm not worried about that. They can take it as they like, but you saw last night that that approach didn't work very well for either Rick Perry or Newt Gingrich."

On Tuesday night, an Obama campaign aide said that despite Romney's victory in New Hampshire, "the premise of his candidacy began to unravel in the last 48 hours," referring to the questions over Romney's business experience.

Romney tops most national polling and is ahead in the latest surveys in South Carolina and Florida.

However, he came under criticism after a speech Monday to the Nashua Chamber of Commerce, when he said he wanted Americans who were unhappy with their health care coverage to be able to switch insurance companies.

"I like being able to fire people who provide services to me," he said. "You know, if someone doesn't give me the good service I need, I want to say, 'You know, I'm going to go get someone else to provide that service to me.' "

The first seven words of that sentence -- "I like being able to fire people" -- provided an enticing sound bite for opponents to attack.

"Gov. Romney enjoys firing people. I enjoy creating jobs," Huntsman said at a campaign stop in Concord on Monday.

Romney Communications Director Gail Gitcho said opponents are taking Romney's remarks out of context -- a point on which Gingrich and Paul defended him Tuesday.

However, the attacks fed the image of Romney that his GOP opponents and Democrats have pushed: That he's a wealthy businessman who can't connect to average Americans.

Vice President Joe Biden touched on that theme Tuesday night, telling New Hampshire voters via teleconference that Romney's firing comment was "probably taken a little out of context," but nonetheless reflected Romney's true sentiments.

"He thinks it's more important for the stockholders and the shareholders and the investors and the venture capital guys to do well than for those employees to be part of the bargain," Biden said.

But Romney said Wednesday, "You've got almost 2 million people that have lost their jobs under this president, median income that has dropped 10% over the last few years." Millions are out of work, and some have stopped looking, he said.

"This is a failed presidency," he said. "People know that. They're going to do their very best to attack whoever the Republican party puts forward. But in the final analysis, they can't defend their record, and it's because of the president's failure that he's going to be replaced, at least in my view."

CNN's Paul Steinhauser, Alan Silverleib, Dana Bash, Kevin Bohn, Tom Cohen, Jessica Yellin and Rachel Streitfeld contributed to this report.