Romney's triumph Saturday in the Nevada caucuses, following his convincing triumph last week in Florida, bolstered the perception that he may be unstoppable in his second bid for the GOP nomination.
Romney's strong showing has Gingrich plotting a Southern revival, while Santorum and Paul seek stronger showings in upcoming caucuses.
The next contests take place Tuesday, with caucuses in Minnesota and Colorado and a non-binding primary in Missouri.
Only Santorum, the former Pennsylvania senator who finished last in Nevada, was on the campaign trail Sunday with events in Minnesota.
Gingrich, now firmly lodged as the runner-up to Romney, appeared on two Sunday talk shows to describe a survival strategy aimed at Super Tuesday on March 6, when more than 400 delegates will be at stake.
The 10 contests that day include primaries in Georgia, Gingrich's home state, and neighboring Tennessee -- Southern states that border South Carolina, where Gingrich scored his only victory so far.
"Our goal is to get to Super Tuesday, where we're in much more favorable territory," Gingrich said on the NBC program "Meet the Press."
Others expressed skepticism that Gingrich can revitalize his chances in the face of Romney's surge since South Carolina's primary.
"There are 17 primaries and caucuses in the next 30 days, and the map is lining up very well for Mitt Romney because here's the bottom line: Everybody knows he's got the best chance to beat President Obama," Virginia Republican Gov. Bob McDonnell said on the CNN program "State of the Union."
Also on CNN, former House Republican leader Dick Armey, who heads the FreedomWorks grassroots conservative group that helped start the tea party movement, said Gingrich's lone primary victory so far was likely to be his last.
"I don't think Newt will be able to replicate that magic moment in South Carolina, because he had a confluence of circumstances that came," Armey said.
Romney, meanwhile, "continues to work along at a steady pace, and we are left with a dilemma that we are not going to get a reliable, small-government conservative out of this nominating process."
Paul and Santorum said Sunday they would continue their campaigns despite trailing far back because Romney, in Paul's words, "doesn't satisfy a lot of people."
Paul noted on the ABC program "This Week with George Stephanopoulos" that the turnout Saturday in Nevada was lower this year than in 2008, when Romney also won the state. A similar lower turnout in Florida this year compared to four years earlier has raised questions about whether Republican voters are unhappy with their choices.
With a dedicated base of mostly young supporters, Paul could represent a valuable voting bloc if the outcome of the nomination race remained undecided at the GOP's August convention.
"Yeah, I think Mitt could change his mind. He's changed his mind in the past," Paul said, referring to Romney's shift to more conservative stances since his years as Massachusetts governor. "If he hears from our young people and voters and we continue this, yeah, he's going to change his mind, if there's a political benefit to it."
Santorum referred to Romney as a "uni-dimensional candidate" on Fox, while on CBS, former New York Mayor Rudy Giuliani cited Romney's past changes on issues as a reason for his inability to win more than 50% support in any contest so far.
"He has changed his position on virtually everything," said Giuliani, who has not yet endorsed anyone for the GOP nomination. "He was a traditional moderate Republican -- strong on fiscal matters, conservative, strong on foreign policy but basically socially moderate -- and he changed all that."
In the early primary and caucus states, Romney polled low among those who self-identified as tea party supporters, while Gingrich drew much of the momentum for his South Carolina primary victory from activists within the grassroots movement.
Recent primaries show the tables have turned.