"These are not cogent thoughts," Santorum said, adding that he feared a "worrisome moment that something's going to pop, and we can't afford that in a nominee."
"I'm steady. I'm solid. I'm not going to go out and do things that you're going to worry about," Santorum said.
The candidates also debated economic proposals, and with it, the focus on Romney's tenure at Bain Capital.
Romney has been criticized by Democrats and some GOP candidates alike for his role at Bain, being portrayed as a corporate raider who profited while people lost their jobs at companies in which the private-equity firm invested.
Romney has defended his time there by saying that four major companies that Bain helped have created more than 100,000 jobs, including 10,000 jobs that were lost.
"Capitalism works. Free enterprise works," Romney said at the South Carolina debate, adding that it felt "kind of strange on a stage like this with Republicans having to explain" how private equity and capitalism works.
Gingrich, who is gaining on Romney's lead in South Carolina, took a local angle as he tried to highlight Romney's time at Bain, saying that the company Georgetown Steel was hurt.
"He cited his experience as a key part of his preparation for being president," Gingrich said. "Those cases ought to be looked at."
Thursday night's debate did see a new topic: SOPA, or the anti-piracy bill that has drawn outrage from Internet users who say that it would unfairly censor websites, and which got a swarm of media attention this week as popular sites went dark in protest.
The mere mention of the topic drew boos from the crowd, and, perhaps not surprisingly, all of the candidates said they opposed the bill. Rep. Ron Paul, who has championed the effort to kill the proposal, said he was glad the other candidates disapproved of it, because "Republicans have unfortunately been on the wrong side of this issue."
Paul, 76, repeatedly clamored for attention, particularly on health care and on abortion (he's a doctor). His supporters in the audience boosted him, too, after three candidates exchanged views on abortion and King tried to move on, they screamed "Paul" until the moderator engaged the libertarian.
One topic that Paul was not eager to talk about was his taxes: He admitted that he has "no intention" of releasing financial documents, because, he said, he'd be "embarrassed" to have his lower income compared with the rest of the candidates.
"I think you know more about me than I know about myself," he said.
By far, as has happened in most of the dozen-and-a-half debates, Gingrich won the most applause throughout. He did it with lines like this: "Elect us and your kids will be able to move out because they'll have work."