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ABC News' Michael Falcone reports:

DETROIT - Could an unlikely alliance of liberal Democrats and conservative groups help put Rick Santorum over the top in Michigan?

With polls and the mood on the ground in Michigan suggesting a nail-biter of a primary on Tuesday, two factors that could offer a boost - even a small one - to Santorum, who is battling Mitt Romney in his home state.

First, a number of prominent social conservative and Tea Party-affiliated groups have mounted independent efforts on behalf of Santorum. Some of those groups have joined forces to maximize their impact, but the vast majority are acting on their own.

Second, Michigan's open primary allows Democrats to cross-over and vote in the Republican contest. For weeks there have been rumblings that at least some Democrats will exercise that option and cast their ballots for Santorum in the hopes of denying Romney a victory in his home state.

Evidently Santorum's campaign is hoping the same thing. The campaign  paid for robo-calls inviting Democrats to cross-over and vote for him. It began began hitting Michigan households on Monday.

"On Tuesday join Democrats who are going to send a loud message to Massachusetts Mitt Romney by voting for Rick Santorum for president," an announcer says.

Michigan Democratic Party Chairman Mark Brewer has predicted cross-over voting will occur in Tuesday's primary, but he has been careful to say publicly that the party has no official role in organizing that effort. That said, the state party sent an e-mail to supporters last week featuring a video clip of two Michigan state legislators inviting - in a tongue-in-cheek way - Democrats to vote in the GOP primary.

The idea is also getting pushed on liberal websites like the DailyKos, which has named the effort to encouraging cross-over voting, Operation Hilarity.

DailyKos founder Markos Moulitsas wrote in a blog item on Monday that "this is a multi-pronged effort to deliver Santorum the victory in Michigan - the first is the big-money campaign to drive Romney's numbers down among independents (who can obviously vote in this primary), and the second is our modest (and yes, controversial) effort to get Democrats to cast very legal and proper votes for Rick Santorum."

Moulitsas added, "This race is obviously so close that a few thousand votes could make the entire difference." (He also sent an e-mail to his Michigan supporter list making the pitch for cross-over voting.)

Even so, if cross-over voting does occur those votes would have to be located in places where the "strategic raiders" would be large enough in number to tip the scales toward Santorum. It's not clear that the forces on the left have organized in a such a sophisticated way. Second, political science research has shown that in other elections cross-over voting generally plays an insignificant role in the outcome.

In the end, the help Santorum is getting from his like-minded friends on the right may make more of a difference.

An alliance of Washington, DC-based groups, including the Susan. B. Anthony List, the Culture War Victory Fund, Catholic Vote, the Campaign for Working Families and Let Freedom Ring are wrapping up a seven-day, 20-city bus tour of Michigan on behalf of Santotrum on Tuesday

Marilyn Musgrave, the former Colorado congresswoman and a leader of the Susan B. Anthony List, said she has detected a tremendous amount of enthusiasm for Santorum as she crisscrossed the state. In an interview with ABC News as her bus made its way to Traverse City on Monday, Musgrave said her coalition's effort are all the more important since "not that many weeks ago it was almost a foregone conclusion that Romney was going to win here."

"You have a window of opportunity and you want to take it and give it all you got," she added, noting that the groups plan to continue the pro-Santorum bus tour in Ohio, Tennessee and Georgia in advance of Super Tuesday.

Fellow bus rider, Maggie Gallagher, the director of Culture War Victory Fund, a new religious liberty organization, observed that Santorum is "becoming more than a candidate, he's becoming a cause."

Tea Party groups across the state have also been faster to embrace Santorum than Romney. Jim Frey of the Southwest Michigan Patriots, a Tea Party-affiliated group based in Kalamazoo, said in an interview today that at a recent caucus meeting of other such organizations, support for Santorum ran high. However, Frey noted that neither he nor his group had any particular get-out-the-vote efforts planned for primary day.

A group from Texas called Eagle Forum, has set up Michigan phone banking operation. And another Tea Party-affiliated organization, Freedom's Defense Fund, circulated an e-mail to supporters over the weekend saying they planned to spend "the next 72 hours calling Michigan voters, identifying Santorum supporters, and getting them out to vote on Election Day."