"I'm going to wait until everyone is voted off the island," he told "Tonight Show" host Jay Leno earlier in the week.
But a top adviser, David Plouffe, went after Romney, the early front-runner in the race. Plouffe, who managed Obama's 2008 campaign, said Romney has "moved all over the place" on issues from abortion to gay marriage over his career and might not have firm enough convictions to make the tough decisions as president.
"You get the sense with Mitt Romney that if he thought it was good to say the sky was green and the grass was blue, to win an election, he'd say it," Plouffe said on NBC's "Meet the Press."
It's not yet clear which of the Republicans might survive the nomination fight. While Cain "seems to have tapped into something," Plouffe said he found it interesting that "Romney continues to have 75, 80 percent of his party looking somewhere else, and so it'll be interesting to see if he can turn that around."
The Romney campaign shot back by saying Obama "can't run on his abysmal economic record and he is desperate to distract from the historic loss of middle-class jobs that has occurred on his watch. Americans won't be fooled by false and negative attacks."
Republicans in Iowa aren't leaning toward any one candidate, even though Romney's essentially been running for president since losing in the state in 2008.
Despite his showing in the Iowa poll, Cain trails both Romney and Perry in fundraising by the millions.
Perry is starting to focus on Iowa with a new ad, and on Sunday, he hit Romney for being on both sides of debates over gun control, abortion and gay rights.
"I have been a consistent conservative," Perry said. "I don't get confused with just telling the truth."
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