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The debate in many ways was more tepid than some of the previous affairs. Coming into the event, the accusations against Mr. Cain overshadow all of the other story lines in the Republican field: first and foremost among them, whether Mr. Cain or someone else can emerge as a serious conservative alternative to Mr. Romney before the nomination process kicks off with the Iowa caucuses in early January.

“This country is looking for leadership and this is why a lot of people, despite what has happened over the last nine days, are still very enthusiastic about my candidacy,” he said.

Asked about whether the accusations would discourage him from supporting Mr. Cain as the head of a company, Mr. Romney took a pass, saying that was up to voters to decide.

Heading into the debate, Rasmussen Reports released a poll suggesting voters think Mr. Romney is on his way to capturing the nomination. In the survey, 45 percent of more than 1,000 Republican and Republican-leaning independents predicted Mr. Romney would win the nomination.

Mr. Cain placed second with 13 percent and Mr. Perry finished third with 9 percent.

The pollster, however, also warned that Mr. Romney remains a weak frontrunner because his base of support essentially has plateaued and he is not generating a lot of enthusiasm among Republicans.

Mr. Gingrich showed flashes Wednesday night of why he is the latest possible “anyone-but-Romney-candidate.”

The former House speaker has relied on a strategy of trying to stay above the daily fray and aiming his attacks at Mr. Obama and the media, while casting himself as an ideas man. In a previous debate he made a point of noting he was exchanging emails with the big thinkers on major issues of the day.

The strategy has allowed him to duck some of the difficult questions that ultimately will come his way if his star continues to rise; namely about his previous support of an individual health care mandate and his extramarital affairs. He also likely will have to defend the global warming commercial where he sits on a couch shoulder-to-shoulder with former House Speaker Nancy Pelosi, California Democrat, and says they “agree our country must take action to address climate change.”

For their part, Democrats remain intent on attacking Mr. Romney. He was greeted Wednesday in Michiigan - a state his father governed in the 1960s - by full-page advertisements in the Detroit Free Press and Detroit News in which the Democratic National Committee criticized his opposition to the 2008 bailout of General Motors and Chrysler.

In the debate, Mr. Romney rejected the notion that voters should be wary of his core convictions and the Democratic charge that he didn’t always oppose the 2008 federal bail out the auto industry.

“I think people understand that I’m a man of steadiness and constancy. I don’t think you’re going to find somebody who has more of those attributes than I do,” he said, before noting his that he has been married for 42 years, has attended the same church his entire life and worked at Bain consulting firm for 25 years.