Rick Santorum, in an interview Sunday with ABC's "This Week," said it's a good thing different candidates won the first three primaries, ensuring there's no clear winner at this stage of the campaign.
"The longer this campaign goes on, the better it is for conservatives, the better it is for our party. We stay focused on the issues, which is going out and taking on Barack Obama. The Republicans are the focus," said Santorum, who won in Iowa. "The idea that conservatives have to coalesce in order to beat Mitt Romney, well, that's just not true anymore. Conservatives actually can have a choice. We don't have to rush to judgment. We can actually look at the candidates."
Mitt Romney, who came in second in South Carolina with 28 percent to Gingrich's 40 percent Saturday, but won New Hampshire, said the job of president of the United States is filled with challenges and he plans to show voters he "can take a set back and come back strong."
Romney said he has signed on for debates Monday and Thursday so Florida primary voters can have a better idea of his stance on the issues.
"I hope that over time, as people see more of me and more of the other guys, that I'll come out ahead," Romney said on "Fox News Sunday." "But if not, that's the way it's going to be."
Gingrich, on CBS' "Face the Nation" said it's his authenticity that will win him the nomination, something he believes Romney lacks.
"I think the number one thing people look for in difficult times is authenticity. They want somebody who is what he seems to be, who is comfortable with himself," Gingrich said. "Governor Romney may be running for CEO. I'm running for president."
Meanwhile, Sen. Jim DeMint, R.-S.C., said that while he still doesn't plan to endorse any one candidate at this point, he thinks Republicans most value Gingrich's fighting spirit.
"It's pretty clear to me, I think Republicans know our country is in deep trouble," he said on CNN's "State of the Union." "And they want a fighter as president. And what they saw in the debate from Newt was that he was willing to take on the media. That gives us a sense that he might be willing to take on the Washington establishment."
New Jersey Gov. Chris Christie Sunday shot down any rumors he might have his eye on a vice presidential nomination.
"I absolutely believe that come November 2012 I'm going to be governor of New Jersey and not in any other office," Christie said on NBC's "Meet the Press."