COLUMBIA, S.C. (AP) – Despite leading in the polls in South Carolina a week before that state’s primary, Mitt Romney’s record at a private equity firm and his advocacy of a health insurance mandate while Massachusetts governor would hobble him as the GOP presidential nominee, several of his rivals said Sunday.

Rick Santorum, Rick Perry and Newt Gingrich all said Romney continued to benefit from the fractured GOP field and the failure of social conservatives to fully coalesce around a single alternative. Gingrich acknowledged that a Romney victory Saturday in South Carolina would give him an “enormous advantage” going forward after back-to-back wins in New Hampshire and Iowa.

Romney was taking a rare day off from campaigning while his opponents focused on the South Carolina coast. They also attended church services and prayer breakfasts in the state, which has a large population of evangelicals and other conservative Christians.

The candidates faced a packed week of campaign events and nationally televised debates Monday and Thursday before the first-in-the-South primary. No Republican has won the party’s presidential nomination without carrying South Carolina.

Santorum, who won the endorsement of an influential group of social conservatives and evangelical leaders Saturday in Texas, said it was imperative for the field to shrink if conservatives had any chance of slowing Romney.

“We feel like once this field narrows and we get it down to a two-person race, we have an excellent opportunity to win this race,” the former Pennsylvania senator told “Fox News Sunday,”

Santorum battled Romney to a virtual tie in Iowa before falling to fifth place in New Hampshire.

Gingrich, a former House speaker, and Perry, the Texas governor, fared poorly in both states but are continuing to compete with Santorum for the support of social and religious conservatives.

All three have the backing of well-financed independent groups known as super political action committee that can help keep their candidacies afloat.

Santorum refused to suggest anyone should drop out of the race as a way to consolidate conservative support behind an anti-Romney candidate. But he said Republicans would have a hard time beating President Barack Obama in November if Romney were the nominee. Santorum cited Romney’s push for mandatory insurance coverage in Massachusetts.

“Romney’s plan, as much as he’d like to say it’s not, was the basis of Obamacare,” Santorum said on CBS’ “Face the Nation.”

“For us to give away that issue with Gov. Romney would be a case, in my opinion, of malpractice on the part of the primary voters in the states to come.”

Gingrich and Perry used television interviews to focus on Romney’s former leadership of the Bain Capital venture firm. Both defended raising questions about Bain’s business practices, saying Romney’s tenure would come under relentless assault from Democrats in the general election.

Romney’s campaign claims he helped create more than 100,000 jobs while heading up Bain. But the campaign cites success stories without laying out the other side — jobs lost at Bain-acquired or Bain-supported firms that closed, trimmed their workforce or shifted employment overseas.

Gingrich said questions about Bain were fair game since Romney has made his experience in the business world the chief selling point for his candidacy.

“It’s fair to raise the questions now, get them out of the way now to make sure that whoever we nominate is clear enough, public enough, accountable enough that they can withstand the Obama onslaught,” Gingrich said.

Gingrich was pressed to defend a film highly critical of Bain that is being aired by super PAC backing his candidacy. Gingrich said he wanted any inaccuracies edited out but refused to call on the film to be taken down.

Gingrich also said he planned to release his tax returns this week and called on Romney, who had refused to do so, to follow suit.

“He’ll never get through the fall without releasing his records,” Gingrich said, insisting the country “deserves accountability and they deserve transparency.”

Perry suggested Obama’s team was eager to attack Romney over his Bain tenure. That was a point Obama campaign adviser David Axelrod confirmed.

“If this is a fatal flaw we need to be talking about it now, not talking about it in September and October,” Perry said.

“The issue is not going to go away and it’s not like we’ve cracked an egg open here for the first time,” Perry said.

At a prayer breakfast in Myrtle Beach, Perry pressed religious conservatives to back his candidacy.

“Who will see the job of president as that of faithful servant to the American people, and the God who created us?” Perry said at the hotel convention center, with Santorum not sitting far from the podium. “I hope each of you will peer into your heart and look for that individual with the record and the values that represent your heart.”

Axelrod portrayed a campaign against Romney as a debate over values and the needs of the middle class.

“Is that the economic vision for this country — outsourcing, off-shoring, stripping down companies, lowering wages, lowering benefits? I don’t think that’s the future for this country,” Axelrod told CNN.

Former Utah Gov. Jon Huntsman picked up the endorsement of The State, South Carolina’s largest newspaper. The paper described him as a “realist” able to appeal to the centrist voters who will decide the general election.

Texas Rep. Ron Paul was returning to campaigning for the first time since Wednesday. He has spent several days at home in Texas after his second-place finish in the New Hampshire primary last week.