Washington (CNN) -- Mitt Romney's front-running campaign on Monday took aim at trailing rival Rick Santorum, suggesting there is concern the conservative Santorum might be poised to do well in this week's Republican presidential contests.
The GOP hopefuls face caucuses in Minnesota and Colorado on Tuesday, along with a nonbinding primary in Missouri. On Saturday, Maine wraps up its caucuses, followed by a break until a February 22 debate on CNN and February 28 primaries in Arizona and Michigan.
Romney strengthened his leading status in the GOP presidential race with a solid victory Saturday in the Nevada caucuses. It was his second straight triumph and third in the five contests so far, bolstering the perception he may be unstoppable in his second bid for the Republican nomination.
Santorum is competing with Newt Gingrich for conservative support in hopes of halting Romney's momentum. He has campaigned hard in Minnesota and in Missouri, a state where Gingrich failed to get on the ballot, to position himself as the leading conservative challenger to Romney.
Santorum told CNN's John King that "doing well and showing that ... we still have a strong base of support out there is going to be good enough for us" on Tuesday.
"We certainly have a chance of winning one or more of those states," he said.
Even Gingrich acknowledged Monday that the former Pennsylvania senator could pull off a surprise victory.
"I think that Santorum is going to have a pretty good day tomorrow, and he will have earned it," the former House Speaker told reporters outside an energy forum in Golden, Colorado.
The Romney campaign responded Monday by putting former Minnesota Gov. Tim Pawlenty on a conference call with reporters to criticize what he called Santorum's legislative history of supporting spending earmarks and increasing the federal debt ceiling.
"He has been part of the big spending establishment in Congress and in the influence peddling," Pawlenty said of Santorum.
The Romney campaign also issued a statement that challenged Santorum's constant attacks on the Massachusetts health care plan implemented while Romney was governor of that state in the 1990s.
It cited reports on FactCheck.org and PolitiFact.com in recent weeks that rated as "not true" or "mostly false" the claims by Santorum that the Bay State health care law created a government-run system.
The two websites also disputed Santorum's assertions that the Massachusetts plan increased premiums and waiting times for patients, and that Romney advocated the Massachusetts model for the entire country.
Santorum's campaign responded with its own statement that repeated some of the claims cited by the Romney campaign. A separate statement from Santorum spokesman Hogan Gidley said Romney's attacks on Santorum showed he was feeling the heat.
"Mitt Romney can't attack Obama on any of those major issues because Gov. Romney agrees with Obama on all of them -- and his attack and smear campaign is his way of avoiding his liberal record," Gidley said in the statement.
Santorum kept up his criticism of Romney on the health care issue, saying at a campaign event in Rochester, Minnesota, that his rival's record on health care makes him a poor choice to run against President Barack Obama in November.
"The problem is that we have a candidate who is running, who is now seen by the media as the prohibitive favorite, who is the worst possible person in this field to put up on this most fundamental issue of this campaign, and that is Gov. Romney," Santorum said, adding later that Romney is "simply dead wrong on the most important issue of the day and should not be the nominee of our party."
Santorum sounded congested in his speech and told the audience that he caught a bug from his 3-year-old daughter, Bella.
"As you can see, I've got my own health care issues," he joked.
In the Nevada caucuses, Santorum finished last among the four candidates, with Romney getting 50% support, while former House Speaker Gingrich had 21%, Rep. Ron Paul had 19% and Santorum was at 10%, according to certified final results released Monday.
However, the attention that Romney's campaign paid to Santorum indicated the dynamics of the Republican race might be shifting, at least for this week's caucuses and primaries.
Ken Buck, a tea party-backed Colorado Republican who failed in his 2010 bid to defeat Democratic Sen. Michael Bennet, said Monday that Santorum appears to be the strongest conservative challenger to Romney in his state.
"I think it's partly the evangelical push, but Santorum is a worker," Buck said of the candidate's appeal to Christian conservatives. "He shows up, he hits a lot of the right places. He is somebody who is viewed as getting out there and meeting with a lot of people."
Romney's strong showing in Nevada left Gingrich to plot a Southern revival to his campaign by focusing on his native Georgia and neighboring Tennessee for support when the biggest single day of the primaries -- Super Tuesday, with 10 states in play -- occurs March 6.
Former House Republican leader Dick Armey, who heads the FreedomWorks grass-roots conservative group that helped start the tea party movement, said Sunday on CNN's "State of the Union" program that Gingrich's lone primary victory in South Carolina is likely to be his last.
On Monday, Gingrich softened the more personal attacks on Romney, even as he told those attending a rally in Golden, Colorado, that he thought the former governor is too moderate to defeat Obama.
"Gov. Romney doesn't represent profound change," Gingrich said, adding that as Massachusetts governor, Romney "basically accommodated liberal Democrats."
"He is not a bad person per se, but he is also not a person who goes in there with force and will and fundamentally changes things," Gingrich continued. "And we are in a situation where we need fundamental change."
Others expressed skepticism that Gingrich can revitalize his chances in the face of Romney's surge in Florida and Nevada.
Along with Santorum, Paul said Sunday he will continue their campaigns despite trailing badly because Romney, in Paul's words, "doesn't satisfy a lot of people."
Paul said 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 with four years earlier, has raised questions about whether Republican voters are unhappy with their choices.
The Texas Republican spent Monday in Minnesota at rallies in St. Cloud and Minneapolis. He reiterated his desire to bring back all troops from overseas conflicts, explained why his message resonates with young supporters and preached his libertarian philosophy.
"Too many people in Washington who have not taken seriously the oath of office, so we've gotten ourselves into a mess," Paul said. "But ... people are realizing it's not working, we're going to replace it with something. And I know exactly what we're going to replace it with: and that is, freedom."
CNN's Jim Acosta, Chris Welch, Peter Hamby, Candy Crowley, Ashley Killough, Gabriella Schwarz and Gregory Wallace contributed to this report.