On the same program, Scott said: "If Romney wins South Carolina, I think the game is over."
After previously describing Romney's former company, Bain Capital, as corporate "vultures," Perry used less harsh language during an appearance on CNN's "State of the Union." He reiterated his accusation, however, that Bain "came in and basically shut down" a South Carolina steel company, taking away "a lot of money in management fees."
Obama's campaign will raise the matter if Romney gets the Republican nomination, Perry warned.
"The issue's not going away," he said. "Now's the time to talk about it, not in September and October."
Gingrich, a former U.S. House speaker, expressed a similar view on NBC's "Meet the Press" and CBS's "Face the Nation."
"Our nominee had better be capable of standing up there, telling the truth, enduring the negative ads and winning the vote," Gingrich said, insisting he is a more accomplished debater and stronger candidate than Romney.
Gingrich also told NBC he would release his tax returns on Thursday, and reiterated his challenge for Romney to do the same -- continuing a campaign to get Romney to disclose details of his substantial personal wealth.
Romney has said he has complied with legal disclosure obligations, but added he might release his tax returns in the future.
Gingrich said it would be better for Romney to release his tax returns now instead of having the issue come to a head in the fall during a one-on-one campaign against Obama.
Santorum, meanwhile, told "Fox News Sunday" that an endorsement on Saturday from Christian conservative leaders should help his campaign, as he seeks to regain the luster of a razor-thin second-place finish behind Romney in Iowa.
Santorum, who finished fifth in New Hampshire, has been fighting with Gingrich and Perry for support from South Carolina's powerful evangelical voters. Saturday's endorsement was intended to unite those voters behind one candidate and avoid a split that would hand Romney a victory despite South Carolina's conservative pedigree.
"It would be helpful if everybody dropped out and I would win," Santorum said. "But, you know, the idea is, we're going to go through this process, people have the right to go out and make the case to the voters and then we'll see what happens."
The American Research Group poll released last week finds Romney and Gingrich in a statistical dead heat in the state.
According to the poll, 29% of likely GOP primary voters say they will support Romney. Another 25% said they would support Gingrich, putting Romney's lead within the poll's sampling error.
The survey indicates Rep. Ron Paul of Texas has 20% of the vote, Perry has 9%, Santorum has 7%, and 7% are undecided.