The social conservative scored an early win last month after a recount handed him 34-vote victory in first-in-the-nation Iowa.
But he failed to carry that momentum, placing at or near the bottom of the narrowing field in New Hampshire, South Carolina, Florida and Nevada.
Presumed frontrunner Mitt Romney appeared to have cemented his lead with resounding wins in Florida and Nevada last week, but Santorum told a crowd of supporters that an upset in Minnesota "can stop the streak."
"Minnesota can reset this race," Santorum told the cheering crowd gathered at a winery outside of the town of Waconia.
A poll released Sunday showed Santorum ahead by two points -- which is within the statistical margin of error.
Since Minnesota holds caucuses -- where voters can't just stop by to cast a ballot but must instead show up for a discussion on Tuesday at 7 p.m. (0100 GMT) -- turnout will be key to winning this midwestern state.
"This room can change the course of this election," Santorum told the 300 or so supporters who skipped watching the Super Bowl to hear him speak.
"If everybody in this building gets 10 people, think about the impact you can have on this race."
Santorum, who earlier Sunday spoke at a church in suburban Minneapolis and visited the rural Minnesota factory that makes his signature sweater vests, stayed more than an hour after his speech to greet and take photos with everyone at the winery.
Approached by AFP, he echoed rival Newt Gingrich's vow to carry the challenge all the way to the Republican convention in June.
"Our intention is to win, so of course we're going to take it to the convention," the former US senator from Pennsylvania said in a brief interview.
Nor does he intend to drop out after if he doesn't sweep the March 6 'Super Tuesday' contest in which 10 states are at stake.
"If we finish in last place in every race, yes, but I don't think we're going to do that," he told AFP. "I think we're going to do very well."
Santorum said he is hoping to be able to consolidate the support of the Republican party's social conservatives, many of whom are uneasy with Romney's more liberal record as governor of Massachusetts.
Santorum had the support of 29 percent of Minnesota Republicans while Romney won 27 percent in the survey from Public Policy Polling.
Gingrich, whose campaign appears to be losing steam, was at 18 percent while congressman Ron Paul held 12 percent, the poll showed.
Minnesota has 40 delegates at stake in its non-binding caucuses, which will select delegates to the Republican convention to choose the party's candidate to face Democratic President Barack Obama in November.
Minnesota is among three heartland states voting on Tuesday, along with Missouri and Colorado.
PPP said Tuesday has the potential to be a big day for Santorum, who has had a lead in Missouri and is running second in Colorado.
But the polling group said Romney -- who is leading national polls -- has momentum after big wins in Florida and Nevada.
A separate PPP poll showed Romney with 40 percent in Colorado to 26 percent for Santorum, 18 percent for Gingrich and 12 percent for Paul.