MANCHESTER, N.H. (CBS/AP) -- The Republican presidential candidates who aren't Mitt Romney brought along modest hopes on their smiling, hand-shaking visits to New Hampshire's polling places Tuesday — just let me come in third place or so, most said, and survive to challenge the front-runner again in South Carolina and Florida.
Romney held on to the demeanor of the overwhelming favorite, despite coming under increasing volleys of criticism from his rivals and suffering an ill-timed, foot-in-mouth moment on the eve of the nation's first presidential primary.
A narrower than expected win for the former Massachusetts governor — or a surprisingly strong finish from one of his opponents — could shake things up. Either would play as more evidence that Republican voters still aren't sold on Romney, who barely squeezed out his first win, in the Iowa caucuses.
A microcosm of such doubts was on display with the first ballots cast, in tiny Dixville Notch, the village that traditionally votes at midnight. Romney and Jon Huntsman each received two of the six votes. One went to Newt Gingrich and the other to Ron Paul, the libertarian-leaning candidate who is dismissed by many Republicans nationally but has been polling in second place in the state for months.
"Dixville Notch might be a harbinger in this race," said Huntsman, a former Utah governor who skipped Iowa to pin his hopes on a strong showing among New Hampshire's independents and moderates.
The rest of New Hampshire voters were going to the polls throughout the day. Donna Parris, 52, an independent from Concord, cast her vote for Huntsman — and against the Romney steamroller.
"The leader of the pack right now, I don't want in there," Parris said, describing Romney as "just a real political-speaking guy that I don't think is going to change anything."
A grinning Gingrich arrived at a polling site in Manchester with wife, Callista, to greet voters but was met instead by a crush of reporters. He compared the crowd to Mardi Gras except "not nearly as much fun." He was visiting polling places throughout the day.
The former House speaker said he expected to finish in the top three or four among the field of six serious candidates, but predicted it would be Romney who would be hurt the most — by falling short of expectations. New Hampshire was expected to be Romney's stronghold, Gingrich said, and "I don't think it's going to be much of a fortress."
But others likely have more on the line in the first primary. Speculation already was mounting about which candidates might be pushed out of the race if they finished below third place.
Rick Santorum, who rocketed to prominence with a virtual tie with Romney in Iowa, said there wasn't time enough to capitalize on that momentum before Tuesday and that he would be content to pull a double-digit percentage of the votes.
There are lots of contests still to come, Santorum said, speaking to reporters between shaking voters' hands at a Manchester polling place. "There's going to be lots of opportunities to rise and fall," he said.
Asked on Fox News Channel if he might pull off second place behind the heavily favored Romney, Santorum said, "Just the mention of that would be beyond our dreams."
Third place was being discussed as the equivalent of a win for much of the field because Paul, the quirky Texas congressman, seemed to have a lock on the No. 2 spot. Visiting a polling place in Nashua, Paul said he expected to win "a real nice second place" and to perhaps be closer on Romney's heels than had been predicted.
Romney dinged himself Monday by declaring that he liked being able to fire people, and his rivals were quick to pounce. But some pulled back from their attacks Tuesday, noting that Romney's clumsy quote actually referred to his support for individuals being able to ditch their health insurance companies for better coverage elsewhere.
Romney's insensitive-sounding comment helped Gingrich on Monday leverage his portrayal of the GOP front-runner as a former corporate raider who enriched himself by looting companies and laying off workers. On Tuesday, though, Gingrich said it was "totally unfair" to take Romney's remark out of context and that he wouldn't do so.
A former governor of neighboring Massachusetts who owns a vacation home in New Hampshire, Romney has long enjoyed a substantial lead in the polls here.
"If I am president of the United States, I will not forget New Hampshire," Romney said at a Monday night rally in Bedford, hinting at the impact of the contest while surrounded on by his wife, children and grandchildren.
None of Romney's rivals has proved to be a consistent and credible threat. The latest to emerge from the pack is Santorum, the former Pennsylvania senator who used a passion for social conservatism and a populist economic message to come within eight votes of Romney in Iowa's caucuses.
New Hampshire, which allows independents to vote in its primary, will help decide whether a candidate with Santorum's focus can appeal to a broader electorate, as would be required in a successful general election. On the other side, Huntsman is relying upon independents and moderate Republicans to fuel a late surge to relevancy.
Polls suggested Huntsman may be on the rise, but New Hampshire voters will decide if it it's too little, too late.
A former ambassador to China in the Obama administration, Huntsman spent the final 48 hours trying to capitalize on a notable debate exchange with Romney. A relentless critic of President Obama, Romney had criticized Huntsman for serving in Mr. Obama's administration. Huntsman countered that he had put his country ahead of partisan politics.
Texas Gov. Rick Perry joined the Romney bashing that intensified over the past few days from South Carolina, where he's been campaigning for the next primary on the calendar. Perry said Tuesday that venture capital firms such as Romney's former company, Bain Capital, "come in and loot people's jobs, loot their pensions, loot their ability to take care of their families. I would suggest they're just vultures."
© 2012 CBS Interactive Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.
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