MANCHESTER, New Hampshire (CNN) -- Decision time in the second round of the Republican presidential race arrived Tuesday in New Hampshire, with former Massachusetts Gov. Mitt Romney saying a victory for him as predicted by polls and pundits would be historic.

The battle for second place loomed as the most hotly contested result, with a surging Jon Huntsman battling three-time candidate Ron Paul and former Pennsylvania Sen. Rick Santorum, the runner-up to Romney at last week's Iowa caucuses.

Former House Speaker Newt Gingrich was considered likely to trail the front-runners, with Texas Gov. Rick Perry conceding the first-in-the-nation primary by campaigning this week in South Carolina -- site of the next contest on January 21.

Final polls close at 8 p.m. ET.

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

"We're hearing that the turnout is steady," Scanlan said. "There aren't lines that are backing up, but people are just constantly moving through the polling places. It's certainly what we would expect during a presidential primary."

The last round of published polls showed Romney with a strong lead in what is basically his home field. Romney told Boston radio station WRKO that winning New Hampshire after Iowa would make history of a sort.

"It will be the first time I think anyone who is not an incumbent in our party would have won Iowa and New Hampshire," Romney said. "So, I've got my fingers crossed. This could be a big night for us."

The first votes were cast just after midnight in the tiny communities of Dixville Notch and Hart's Location. In Dixville Notch, Romney and Huntsman, the former Utah governor and ambassador to China, led with with two votes each, while Romney edged Paul 5 to 4 in Hart's Location.

Paul, a Texas congressman, and Gingrich won one vote each in Dixville Notch. Huntsman placed third with two votes in Hart's Location, while Gingrich and Perry got one vote each.

Obama received all the votes in the Democratic primary in both locations.

Huntsman, who skipped last week's Iowa caucuses to campaign heavily in New Hampshire, told CNN his showing in Dixville Notch was "a harbinger of things to come."

"Tonight, we have to make the market move in New Hampshire," said Huntsman, who was running neck-and-neck with Paul for second place in the final polls. "We have to exceed expectations, and if you can exceed expectations in New Hampshire, which is a broad-based primary turnout, then you'll light up South Carolina and the states beyond."

One of New Hampshire's more than 300,000 "undeclared" or independent voter, Linda Underhill, told CNN on 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."

Meanwhile, Gingrich argued that a Romney showing in the 30% range, as the most recent polling suggests, could hurt the front-runner even if he wins 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.

Though Romney has said his work at the Boston-based private equity firm ultimately led to the creation of 100,000 jobs, Gingrich said Romney's pursuit of wealth exacted a huge cost.

Asked about the Gingrich attacks, Romney told WRKO on Tuesday that the negative ads "will not help" Gingrich.

"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.

On Monday, Romney accused Gingrich and others of joining Obama in attacking the free enterprise system by criticizing his business background.

Gingrich wasn't alone in attacking Romney's business record, however. 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."

Romney got a mere eight more votes than Santorum in the Iowa caucuses, while Paul finished a strong third. The libertarian doctor and Congress member has touted his plan to downsize government and chided the frontrunners for being unwilling to push for the kind of overhaul he believes Washington needs.

Santorum, meanwhile, saw his New Hampshire poll numbers surge from single digits to the low double digits after his near-win in Iowa. However, was downplaying expectations for Tuesday night.

"We haven't spent a penny on broadcast television here in New Hampshire. We've only spent five days campaigning here in the last month. We just came here starting at two or three points pretty much tied with Rick Perry in New Hampshire. We've been working hard and now into the double digits. Hopefully we can finish well," Santorum said.

Romney tops most national polling and is ahead in the latest surveys in South Carolina and Florida, the next two states to hold contests following New Hampshire. But he took new criticism Monday after a speech 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," dangled like low-hanging fruit, and some of Romney's rivals pounced.

"Governor 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. But the attacks have 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.

"The language was a little bit clumsy and open to misinterpretation and that might raise some questions about whether or not he's the right person to debate Barack Obama, which I think is an essential characteristic for this fall, but nonetheless, I thought it was unfair to suggest that he actually liked firing people," Gingrich said.

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