"Minnesota is going to change the direction of this race," Santorum told a crowd of around 200 supporters gathered in a Minneapolis suburb.
Santorum, who has seen his campaign flag after triumphing in the first vote of the 2012 White House race in Iowa, is hoping to carry Minnesota with the help of its evangelical Christian and ultraconservative Tea Party voters.
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He has campaigned heavily here and polls were showing the former US senator from Pennsylvania with an unexpected lead of 33 percent to 24 percent for Mitt Romney, who is so far the frontrunner to be the Republican nominee in the November elections.
"For years, Republicans were always told you have to compromise -- you have to pick someone who's a moderate," Santorum said. "Now you have the opportunity to actually nominate someone who agrees with you."
Romney's campaign has already tried to downplay the anticipated loss, with a statement noting "unlike the other candidates, our campaign has the resources and organization to keep winning over the long run."
Romney has concentrated his energies on Colorado -- where he was polling at 37 percent and Santorum was second with 27 percent -- which was also holding a non-binding caucus on Tuesday.
"Governor Romney has been bullying his way through the primary spending on average five times more than his opponents," Santorum said. "He's not inspiring."
Santorum pointed to a national Rasmussen poll released Tuesday which showed him beating Democrat Obama by one point in November as proof that Republicans should vote with their conscience and pick a "true conservative."
Romney is trailing Obama by six points and Obama beat former House speaker Newt Gingrich by 11 points in recent national polls.
"The reason we're going to win is because our viewpoints, our vision of America -- believing in faith and family, believing in building America from the bottom up -- is what the majority of Americans believe," Santorum said.
"President Obama can't hide from his horrible record of job creation... crushing individual liberty and what he's done to undermine the family in this country."
