Gingrich told an enthusiastic crowd of about 300 that he wants "free enterprise that is honest. I want a free enterprise system that is accountable."
Texas Gov. Rick Perry, mindful that some conservatives are unhappy with him for labeling Romney a "vulture capitalist," struck a defensive tone Wednesday but stood by his criticism.
"I understand restructuring. I understand those types of things," Perry told supporters outside Columbia. "But the idea we can't criticize someone for these get-rich-quick schemes is inappropriate from my perspective."
While predicting that South Carolina will be "an uphill battle" for him, Romney projected self-assurance after his big victory in New Hampshire that must be wearing on his five opponents. He dismissed much of their criticism as acts of desperation.
And he said that while other campaigns can afford to stay in the nomination fight for now, "I expect them to fall by the wayside eventually for lack of voters."
Romney's campaign announced that he's raised $56 million for the primary and is sitting on $19 million in cash, dwarfing the other campaigns.
Despite the rougher tone and tougher ideological terrain ahead, the former Massachusetts governor is hoping to force his opponents from the race by achieving a four-state streak with victories in South Carolina on Jan. 21 and Florida 10 days later.
He posted a double-digit win Tuesday night in New Hampshire after a squeaker the week before in Iowa making him the first non-incumbent Republican in a generation to pull off the back-to-back feat.
The way ahead passes through minefields that held him to fourth place in the South Carolina primary when he ran four years ago: Republicans skeptical of his Mormon faith and reversals on some social issues.
Tapping into the state's religious fervor at his Rock Hill rally, Gingrich pledged to fight "anti-Christian bigotry."
Perry was pushing his patriotism. He highlighted his service as an Air Force pilot with a new TV ad in South Carolina featuring veterans praising his character. "I'm the outsider who's willing to step on some toes," Perry says in the commercial.
All the candidates planned to campaign in the state Wednesday. Romney, Gingrich and Perry were being joined there by Rick Santorum, Ron Paul and Jon Huntsman. Perry, who didn't invest much time in New Hampshire while putting his post-Iowa focus on South Carolina, was already waiting for them there.
Several of Romney's rivals have made clear they will seek to undercut the chief rationale of his candidacy: that his experience in private business makes him the strongest Republican to take on President Barack Obama on the economy in the fall. Perry, for one, is accusing Romney of "vulture capitalism" that led to job losses in economically distressed South Carolina.
Obama's team, treating Romney as their likely general election opponent, has joined in the effort to darken the picture of his days in private enterprise. Vice President Joe Biden said Tuesday night that Romney had worried more about investors doing well than he did about the employees of companies bought by his venture capital firm.
On Wednesday, Romney offered a practical-minded defense of layoffs that might not reassure voters worried about holding onto their jobs.
"Every time we had a reduction in employment it was designed to try and make the business more successful and, ultimately, to grow it," Romney told ABC's "Good Morning America."
He got some support from an unusual source his rival Paul, who finished second in New Hampshire. The libertarian-leaning congressman from Texas said other Republican candidates were slamming Romney for market-oriented restructuring of corporations.
"I just wonder whether they're totally ignorant of economics or whether they're willing to demagogue just with the hopes of getting a vote or two," Paul told MSNBC on Wednesday.
Romney said his opponents sound like Obama and other Democrats attacking the free enterprise system and encouraging jealousy toward the wealthiest 1 percent of Americans. "It's a very envy-oriented attack," he told NBC's "Today" show.
Romney contends the criticism actually works to his benefit by highlighting the business acumen that will help him set the nation's economy right and shrink the federal government.
TV ads are filling the South Carolina airwaves, including negative spots like a new one from Gingrich assailing Romney for switching his position on an issue that resonates strongly with evangelicals who make up the base of the GOP here.
"He governed pro-abortion," the Gingrich ad says. "Massachusetts moderate Mitt Romney: He can't be trusted."
About $3.5 million already has been spent on TV ads in South Carolina, the bulk of it by Perry and a supportive super PAC. But that doesn't count the $3.4 million a pro-Gingrich group has pledged to spend to go after Romney, or the $2.3 million a pro-Romney group plans to spend in the coming days. Santorum and a super PAC friendly to him also are pouring money into the state, as is an outside group working on Huntsman's behalf.
Expect a flood of more hard-hitting commercials primarily aimed at the front-runner in a state known for brass-knuckled Republican politics.
For all of Romney's challenges, the presence of a cluster of socially conservative candidates fighting to be his chief alternative could work in his favor by splitting the vote on the party's right flank. Santorum, Gingrich, Perry and others split the faith-focused vote in Iowa. South Carolina also has a large contingent of evangelical voters, some of whom remain suspicious of Romney.
"I don't know if we can win South Carolina," Romney said Wednesday on ABC. He added, "I know it's an uphill battle."
South Carolina could end up being the last stop for some candidates. Perry, for one, has had back-to-back dismal showings and is looking to South Carolina to right his struggling campaign.
Gingrich, the former Georgia lawmaker, is also playing on his regional ties.
Santorum and Huntsman also have vowed to press on. Santorum wants to claim the conservative mantle; Huntsman eschews ideological labels and is selling himself as someone who can heal a polarized nation.
Associated Press writers Shannon McCaffrey and Brian Bakst in South Carolina and Connie Cass in Washington contributed to this report.