Perry referred to a steel mill in Georgetown, S.C. where, he said, "Bain swept in, they picked that company over and a lot of people lost jobs there."
Romney said the steel industry was battered by unfair competition from China. As for other firms, he said, "Four of the companies that we invested in ... ended up today having some 120,000 jobs." And he acknowledged, "Some of the businesses we invested in were not successful and lost jobs."
It was Perry who challenged Romney to release his income tax returns. The Texas governor said he has already done so, and Gingrich has said he will do likewise later in the week.
"Mitt, we need for you to release your income tax so the people of this country can see how you made your money. ... We cannot fire our nominee in September. We need to know now," Perry said.
Later, a debate moderator pressed Romney on releasing his tax returns. His response meandered.
"If that's been the tradition I'm not opposed to doing that," Romney said. "Time will tell. But I anticipate that most likely I'm going to get asked to do that in the April time period and I'll keep that open."
Prodded again, he said, "If I become our nominee ... what's happened in history is people have released them in about April of the coming year, and that's probably what I'd do."
April is long after the South Carolina primary and the Republican nomination could easily be all but decided by then, following Super Tuesday contests around the country in March.
Santorum stayed away from the clash over taxes, instead launching a dispute of his own. He said a campaign group supporting Romney has been attacking him for supporting voter rights for convicted felons, and asked Romney what his position was on the issue.
Romney initially ducked a direct answer, preferring to ask Santorum if the ad was accurate.
He then said he doesn't believe convicted violent felons should have the right to vote, even after serving their terms. Santorum instantly said that as governor of Massachusetts, Romney hadn't made any attempt to change a law that permitted convicted felons to vote while still on parole, a law the former Pennsylvania senator said was more liberal than the one he has been assailed for supporting.
Romney replied that as a Republican governor, he was confronted with a legislature that was heavily Democratic and held a different position.
He also reminded Santorum that candidates have no control over the campaign groups that have played a pivotal role in the race to date.
"It is inaccurate," Santorum said of the ad assailing him. "I would go out and say: 'Stop it. That you're representing me and you're representing my campaign. Stop it.'"
That issue returned more than an hour later, when Gingrich said he too has faced false attacks from the same group that is criticizing Santorum. He noted that Romney says he lacks sway over the group, "which makes you wonder how much influence he would have if he were president."
Romney said he hoped no group would run inaccurate ads, and he said the organization backing Gingrich was airing a commercial that is so false that "it's probably the biggest hoax since Bigfoot."
He called for scuttling the current system of campaign finance laws to permit individuals to donate as much money as they want to the candidates of their choice.
Noting that the debate was occurring on Martin Luther King Jr. Day, one moderator asked Gingrich if his previous statements about poor children lacking a work ethic were "insulting to all Americans, but particularly to black Americans."
"No," Gingrich said emphatically, adding his aim was to break dependence on government programs. "I'm going to continue to find ways to help poor people learn how to get a job, learn to get a better job and learn someday to own the job," he said.
Romney is the leader in the public opinion polls in South Carolina, although his rivals hope the state's 9.9 percent unemployment rate and the presence of large numbers of socially conservative evangelical voters will allow one of them to slip by him.
Associated Press writer Dave Espo contributed to this report.
Follow Shannon McCaffrey at www.twitter.com/smccaffrey13
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