Mitt Romney’s rivals tried to shove one another aside Tuesday in an effort to consolidate support around a single conservative alternative to the former Massachusetts governor.

Not surprisingly, there was disagreement among the three men — former House speaker Newt Gingrich (Ga.), former senator Rick Santorum (Pa.) and Texas Gov. Rick Perry — over who ought to do the shoving and who ought to do the stepping aside.

Gingrich, coming off a fiery and widely praised performance in Monday night’s debate, was particularly aggressive in suggesting that Santorum and Perry should bow out, arguing that a vote for either is essentially a vote for Romney because they can’t win.

Santorum noted that there have been two contests so far and he’s beaten Gingrich in both, so he wasn’t in any mood to take his advice.

Perry lumped the two together and said both were Washington insiders. South Carolinians would come around to his outsider effort, he said.

Former Alaska governor Sarah Palin added a twist to the contest Tuesday night, saying she would vote for Gingrich in the South Carolina primary if she could. Palin, the GOP’s vice presidential nominee four years ago, has not formally endorsed a candidate.

“In order to keep this thing going, I’d vote for Newt and I would want this to continue — more debates, more vetting of candidates, because we know the mistake made in our country four years ago was having a candidate who was not vetted to the degree that he should have been,” she told Fox News’s Sean Hannity.

It was not clear whether she was referring to Barack Obama or another candidate.

The inability of the candidates or voters to coalesce around a single conservative leaves in place the splintered dynamic that has enabled Romney to remain at the front of the field. The last-minute sniping made it appear increasingly unlikely that any of the three would break from the pack, potentially leaving Romney with a clear path to victory in Saturday’s primary.

“At this point, it’s a low chance that anyone would truly consolidate conservative support,” said Joel Sawyer, a former executive director of the South Carolina Republican Party who until Monday was supporting former Utah governor Jon Huntsman Jr. “Nobody has really been able to put a dent in Romney.”

The GOP race is playing out in much the same way it did in 2008, when Sen. John McCain defeated an equally divided conservative field in South Carolina and went on to capture the nomination.

Sawyer said the contenders have spent so much time bashing one another that “this is a play for second . . . rather than going after the front-runner.”

With time running out, Gingrich argued Tuesday that he is the only candidate who has a realistic shot at beating Romney. Recent polls have showed Gingrich running ahead of Santorum and Perry in the Palmetto State.

“Any vote for Santorum or Perry is, in effect, a vote to help Romney become the nominee,” he said at an event at an art gallery in Florence on Tuesday. Later, in Aiken, he noted: “The only reason that Governor Romney is ahead at this moment is that the conservatives are split three ways.”

In an e-mail to supporters after the Monday debate titled “Newt’s Back!!,” his team called his standing-ovation-earning performance a sign that only he has the chops to take on President Obama. “Since defeating Obama is so important, what do we have to do to nominate someone who is conservative enough and tough enough and clear enough to defeat Obama?” Gingrich said to reporters.

But Santorum insisted that Gingrich is in no position to offer him advice.

“I think someone who’s lost two elections to me so far shouldn’t be telling the person he’s lost two elections to to get out of the race,” he said. Santorum came within eight votes of Romney in Iowa. New Hampshire results are not yet certified. Election-night tallies showed Gingrich edging out Santorum for fourth place, but more recent numbers put Santorum a bit ahead; they essentially tied.

At a Republican luncheon in Aiken, a voter asked Santorum whether there was “anything conservatives can do, for the good of the country, to coalesce” around one candidate.

“We really, really don’t want Romney to win,” the woman said, as a good portion of the 300-person crowd applauded.

Santorum responded that Gingrich has not been a reliable conservative, noting his past support — now disavowed — for a health-insurance individual mandate and a Social Security plan that would worsen the national debt.

“We have Governor Romney, who’s timid and isn’t what the country needs,” Santorum said. “Then you have Newt, who’s bold but all over the place. Attacking capitalism, supporting capitalism. Against global warming, for global warming. We need someone who’s bold and consistent.”

Santorum is holding out hope that a canvass of the vote in the Iowa caucuses, expected to be complete by week’s end, might show that he defeated Romney there.

That news could give his flagging effort a boost going into Saturday’s vote and puncture Romney’s narrative about the inevitability of his nomination.

Perry, who also turned in a strong debate performance Monday evening, called Santorum “a good father” and a “good Catholic.” But he said Santorum “hasn’t always been a good conservative.”

Speaking to reporters at the Drive In restaurant in Florence, Perry criticized Gingrich and Santorum for using earmarks to appropriate federal funds for their home states.

“I think the people of South Carolina have to figure it out,” Perry said. “The tea party individuals know you’re not going to change Washington unless you bring an outsider like myself in, who’s not wedded to the old way of doing business — the Wall Street, Washington cabal that’s been calling the shots and created this huge debt and the problems of government that’s too big.”

Allan Louden, who teaches political communication at Wake Forest University in Winston-Salem, N.C., said the tone on the airwaves is significantly harsher than in past presidential primaries, thanks to independent super PACs, making it harder for voters to coalesce around any of the candidates.

“You’ve been given a reason to reject each of them,” he said. “You watch the ads, and they’re just plain vicious. But you also have the sense that they’re not entirely wrong.”

Staff writers Dan Balz and Philip Rucker in South Carolina contributed to this report.