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Despite barreling forward with two back-to-back persuasive victories, Mitt Romney could face a significant challenge in the races ahead, including in Minnesota, where Rick Santorum may have an advantage over the front-runner in a state where Republicans have turned decidedly conservative following a bitter government shutdown last year.

In all 17 states will vote in the next 30 days. Three states go to the polls on Tuesday.

Colorado and Minnesota are holding caucuses. Missouri is holding a primary, but delegates won't be assigned for another month when the state party holds its caucuses. Tuesday's vote is followed by a caucus election in Maine next weekend. It's during this week that Romney's lesser funded rivals will try to turn their fortunes.

The first five voting states were "sort of cast in stone" because they were already staked out by Romney and Paul, who had the advantage of running four years ago and spending a lot of time and money this year, Santorum said. The real race starts now.

"Now, we're getting to the states where people don't have the natural advantage, don't have the time commitment, the staff commitment to really build out an organization like they did in these first five," he told "Fox News Sunday."

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"I think we're going to do very well here in Minnesota. I think we're going to do very well in Colorado, and we've got a one-on-one matchup against Mitt Romney in Missouri. While there's no delegates, it is a key state, it is a primary. And we think we can do exceptionally well in the state of Missouri," Santorum said.

Romney campaigned four years ago as the more conservative choice than Arizona Sen. John McCain. This time around, Romney is the mainstream candidate up against more conservative rivals -- Santorum and former House Speaker Newt Gingrich

"The latest polling data that has come out has Rick Santorum at the top," said Minnesota Rep. Michele Bachmann, who ran as a presidential candidate until dropping out following a last-place finish in Iowa. Bachmann said she thinks the Minnesota race shows that the primary battle is far from over.

"It looks as though there's a closing in. Some of these states are opening up," she told Fox News.

According to Public Policy Polling, a Democratic firm, Santorum is running two points up in Minnesota in a poll released Saturday. But Romney is six points up in Maine and 14 points up in Colorado from his nearest rival, PPP shows in polls from those states.

Still, the other candidates are also betting on a topsy-turvy vote in the less predictable states.

Gingrich, who is trying to get enough money to stay in the race, said grassroots are his strength in the rest of the states, where enthusiasm is the key.

"My job all the way to Super Tuesday and then beyond to Texas, my goal is with Gov. Perry's help and others, to have -- basically be about tied in delegates around the time we come out of Texas," Gingrich said on CBS' "Face the Nation."

J.C. Watts, a former Oklahoma Republican congressman and Gingrich backer, acknowledged the challenges ahead.

"Super Tuesday is obviously going to be pretty critical. I was in Minnesota last week, spent some there. We feel pretty good about our chances there. We felt like Nevada was going to be tough. Colorado is probably going to be tough. But we think we are competitive in Minnesota and Arizona and then spring board us to Super Tuesday, and we expect the results to be much better," he told "Fox News Sunday."

But some of the predictions may be wishful thinking. With just one debate this month, in Mesa, Ariz., on Feb. 22, voters go to the polls in Arizona and Michigan, where Romney's father once served as governor, on Feb. 28.

If the candidates can hold out, March 6 is Super Tuesday, in which 10 states vote, including Virginia, where only Romney and Paul qualified to be on the ballot.

"February is really the death march for second- and third-tier candidates," Republican strategist Rich Galen told The Associated Press. "If Romney sweeps February, the arc of his effort will be so strong, for most Republicans it will be over."