Romney was born and raised in Michigan and his father was a popular governor, but conservatives are threatening to deliver the state to Rick Santorum, who is running neck-and-neck with Romney in the polls in the final hours before voting begins.
Most Michigan polls close at 8 p.m. EST (midnight GMT).
Arizona votes as well on Tuesday and Romney has a comfortable lead there, aided by the man who beat him in the 2008 Republican presidential campaign, Arizona Senator John McCain.
All eyes are on Michigan because a victory for Santorum on what is essentially Romney's home turf would raise questions about Romney's candidacy a week before a defining day of the 2012 campaign, March 6, the "Super Tuesday" when 10 states hold contests.
"I am going to win in Michigan and I'm going to win across the country," Romney said on Monday.
His aides, contemplating the possibility of a defeat, believe Romney could survive a loss in Michigan should it occur because of this year's elongated nomination process.
"The bottom line is you want to win it but it is not as devastating as you guys want to make it out to be if we don't," said a senior Romney strategist.
Santorum, a former Pennsylvania senator, has made himself competitive in Michigan by pressing his conservative views on social issues and by spreading a blue-collar message about the need to rebuild the manufacturing base in the hard-hit Midwestern state.
"We've been traveling all over the state, and I'm really excited about the response. I think we're going to surprise a few people tomorrow night," Santorum said on Monday.
A Santorum win could upend the race and prompt the Republican establishment - concerned that Santorum's strong religious conservatism could make him unelectable - to search for a new candidate to join the race.
An unpredictable factor in Michigan was the ability of Democrats to vote in the Republican primary and try to thwart Romney by voting for Santorum, who many see as having little chance of defeating Democratic President Barack Obama in the November 6 election should he become the Republican nominee.