(CNN) -- Mitt Romney claimed a much-needed victory in Tuesday's Michigan Republican primary, making the race for the GOP presidential nomination anybody's game.

Mitt Romney speaks to supporters after his Michigan win. more photos »

"Tonight marks the beginning of a comeback -- a comeback for America," the former Massachusetts governor said.

"Let's take this campaign to South Carolina and Nevada and Florida and all over the country. Let's take it all the way to the White House," he said to a cheering crowd.

Some political analysts said Michigan was a must-win for Romney, who finished second in Iowa and New Hampshire.

Romney, who won the overshadowed Wyoming caucuses, is a Michigan native and his father was governor of the state in the 1960s.

Forty-one percent of people who voted in the GOP primary said Romney's Michigan ties were important to them, according to exit polls. Watch Romney declare victory »

With 81 percent of precincts reporting, Romney had 39 percent of the vote compared to Arizona Sen. John McCain's 30 percent. Former Arkansas Gov. Mike Huckabee had 16 percent of the vote, followed by Texas Rep. Ron Paul with 6 percent. Former Tennessee Sen. Fred Thompson had 4 percent, and former New York Mayor Rudy Giuliani trailed with 3 percent.

Despite receiving little support from Michigan, Giuliani was happy, according to Steve Forbes, the national co-chair of the Giuliani campaign.

Giuliani has largely skipped the early voting states and devoted his resources to Florida and the delegate-rich "Super Tuesday" states that hold primaries February 5.

"I think the McCain defeat tonight simply underscores how volatile this race is -- how fluid it is, and also underscores how wise Rudy Giuliani was to focus on Florida. We're going to do very well [in Florida]. That means he'll do well on February 5, and that means we're going to get the nomination," Forbes said. Check out the CNN analysis of the results »

Huckabee congratulated Romney after his win, but pledged to take South Carolina's January 19 Republican primary. Watch Huckabee say he's not disappointed »

"It looks like I won Iowa. John McCain won New Hampshire. Mitt Romney won Michigan. But ladies and gentleman, we're going to win South Carolina," Huckabee said.

McCain, who won Michigan in 2000, told his supporters he "didn't mind a fight."

"We're ready for the challenge ahead," he said. "We fell a little short tonight, but we have no cause to be discouraged." Watch McCain congratulate Romney »

On the Democratic side, CNN projected that Sen. Hillary Clinton would win Michigan. See scenes from Michigan's primary »

The New York senator was the only front-runner on the ballot.

Party officials voted to strip Michigan of its Democratic delegates for its decision to schedule the primary so early.

In a show of solidarity with the party, the top-tier Democratic presidential candidates, except for Clinton, asked that their names be removed from the ballot.

But some Democratic leaders in the state urged supporters of Sen. Barack Obama of Illinois and former North Carolina Sen. John Edwards, Clinton's closest rivals, to vote "uncommitted" in the primary.

Under state law, their supporters cannot cast write-in votes for them. But if at least 15 percent of the voters in a congressional district opt for "uncommitted," delegates not bound to any candidate could attend the national convention. That could allow Edwards or Obama supporters to play a role in candidate selection -- if the national party changes its mind and decides to count Michigan's delegates.

With 81 percent of precincts reporting, Clinton had 57 percent of the vote and 38 percent of Democratic primary voters had selected "uncommitted." Ohio Rep. Dennis Kucinich received 4 percent of the vote.

In 2008, more than in recent campaigns, the delegate count may prove important. Narrow losses -- which still add to a candidate's delegate total -- could keep more than one hopeful in contention.

"For the first time since 1988, this is a delegate race," Clinton aide Howard Wolfson said last week.

Romney was expected to win at least 12 Michigan GOP delegates, according to CNN estimates. McCain was expected to win at least 9. Nine of 30 delegates had not yet been allocated.

Most of Michigan's Republican voters had the same thing on their mind -- the economy, according to exit polling.

A majority of Michigan Republican primary voters -- 55 percent -- said the economy is the most pressing issue facing the nation.

That compares to 18 percent who said Iraq, 14 percent who named illegal immigration, and 10 percent who pointed to terrorism.

Michigan has one of the highest unemployment rates in the country -- 7.4 percent, compared with 5 percent nationally -- and the top-tier Republicans vowed to make the revival of Michigan's economy a priority.

The next contests come Saturday, when the Democrats face off in Nevada and the Republicans fight for South Carolina.

The wide-open GOP race is a sign of ongoing dissatisfaction with the Republican electorate, according to Ari Fleischer, former press secretary for President Bush.

"I think South Carolina will be inconclusive. It's not going to be what it used to be because it's too much of a jumble. Florida will be a vital springboard to February 5," Fleischer said. E-mail to a friend

CNN's Peter Hamby, Alexander Mooney, Rebecca Sinderbrand, Mary Snow and Alexander Marquardt contributed to this report.

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