By Andrew Stern

GRAND RAPIDS, Michigan (Reuters) - Republicans in Michigan voted in the U.S. presidential race on Tuesday, with native son Mitt Romney battling for political survival in a primary that could either revive or sink his campaign.

As the results roll in from Michigan soon after the last polls close at 8 p.m. EST (1:00 a.m. British time on Wednesday), Democratic White House contenders Barack Obama, Hillary Clinton and John Edwards are scheduled to meet in an evening debate in Nevada -- site of the party's next contest on Saturday.

The hectic schedule reflects the heightened intensity of the wide-open U.S. presidential race, as both parties choose candidates for the November election to succeed President George W. Bush.

Polls show Romney, a former Massachusetts governor who was raised in Michigan as part of a famous political family, running neck-and-neck with Arizona Sen. John McCain in a state where the ailing economy has moved to the top of the agenda.

A Reuters/C-SPAN/Zogby poll released early on Tuesday gave McCain a statistically insignificant 1-point edge, 27 percent to 26 percent, over Romney. Former Arkansas Gov. Mike Huckabee was third with 15 percent.

Romney needs a breakthrough win in Michigan where his father was a top auto executive and popular governor in the 1960s to keep his White House hopes alive after second-place finishes in Iowa and New Hampshire.

A McCain win after last week's New Hampshire victory would thrust him into the front-runner's role heading into Southern contests in South Carolina and Florida.

"This is a big day. This is a day that I believe will change our nation," Romney said at a rally in an office furniture warehouse.