"Anybody up here could beat Obama," said Paul, whose views verge on libertarianism and who has struggled to expand his appeal.

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Bachmann, who was quicker than any other candidate to criticize a rival, bristled when challenged repeatedly on the accuracy of her facts. "I am a serious candidate for president of the United States, and my facts are accurate," she said.

Indeed, the big question in the opening moments of a fast-paced, two-hour debate went to the heart of a dilemma that could eventually settle the race: Do conservative Republican caucus and primary voters pick a candidate with their hearts, or do they look elsewhere if they judge their favored candidate might not be able to defeat the president?

Those voters begin making that choice on Jan. 3, and if experience is any guide, one or more of the presidential hopefuls on the debate stage will not make it out of Iowa to compete in the New Hampshire primary a week later.

Gingrich, who seemed an also-ran in the earliest stages of the race, has emerged as a leader heading into the final stretch of the pre-primary campaign. His decades in Washington and his post-congressional career as a consultant have been the subjects of tough critiques from Romney's campaign in the past week.

But the former speaker passed up an offer to criticize his rival on the issue of Medicare, saying, "I'm not in the business of blaming Gov. Romney." In fact, he said, Romney has made constructive suggestions for preserving the program that tens of millions of Americans rely on for health care yet faces deep financial woes.

Gingrich drew criticism earlier in the year for calling a GOP Medicare proposal "right-wing engineering." Romney refrained from criticizing that plan but did not embrace it in full.

Bachmann, who has long-since faded to the back of the pack in the polls, showed no such reluctance.

When he labeled her charges inaccurate, she shot back that when she made similar contentions in the previous debate, she was judged factually accurate by an independent arbiter — a claim that the website Politifact deemed inaccurate. She said Gingrich's work for Freddie Mac was in furtherance of a "grandiose scam" to keep alive an entity at the heart of the housing crisis.

"I will state unequivocally for every person watching tonight: I have never once changed my positions because of any payment," Gingrich said, adding that, in fact, he favored breaking up both Fannie Mae and Freddie Mac, his benefactor.

Moments later, Bachmann challenged Paul even more aggressively, saying his refusal to consider pre-emptive action to prevent Iran from getting a nuclear weapon was dangerous.