Meanwhile, Romney is running strong in New Hampshire, which holds the nation's first primary on Jan. 10. Romney is also seen by most conservatives at this point as having the greatest chance of defeating President Barack Obama next year.

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But Romney continues to be viewed with suspicion by many conservatives who say he has changed his stance on such critical issues as abortion and health care. Santorum acknowledged Sunday that Romney has embraced more conservative positions on issues.

"The question is, you know, what's the sincerity of the move and whether he can be trusted," said Santorum.

Bachmann said it was too soon to declare anyone a true front-runner because the dynamic in the race was constantly changing.

"We've got 30 days," she said. "That's an eternity in this race."

Reince Priebus, the Republican Party chairman, said Sunday that he was indifferent to Cain's departure and that it was "only natural" in the face of falling poll numbers and trouble raising money.

This week's agenda for the primary candidates included a stop in Arizona by Romney and a forum Wednesday by the Republican Jewish Coalition in Washington, which is expected to attract Bachmann, Gingrich, Huntsman, Perry, Romney and Santorum. Gingrich was scheduled to meet Monday with real-estate mogul Donald Trump at Trump's New York offices. Trump, who briefly entered the primary race in the spring and drew considerable publicity when he questioned the validity of Obama's birth certificate, said he would moderate a Republican presidential debate in Iowa on Dec. 27.

Paul, who has clashed publicly with Trump, said he thought the GOP was making a mistake in giving Trump so much credibility.

"I don't understand the marching to his office. I mean I didn't know that he had an ability to lay on hands, you know, and anoint people," Paul said.

Paul and Bachmann spoke on CNN's "State of the Union." Santorum spoke on ABC's "This Week." Priebus spoke on NBC's "Meet the Press."