WASHINGTON (AP) — Given to awkward utterances, Republican presidential hopeful Mitt Romney sized up his Michigan primary victory with memorable precision.

"We didn't win by a lot, but we won by enough," he told cheering supporters Tuesday night after eking out a hard-won triumph in his native Michigan over a determined Rick Santorum.

Certainly not nearly by enough to send Santorum, Newt Gingrich or Ron Paul to the sidelines in the most turbulent Republican presidential race in a generation.

But enough to restore some of the lost luster to his own candidacy as the race points toward next week's Super Tuesday — 10 contests in all regions of the country. And likely enough to quell some of the talk about a late entrant into the race, even as party officials continue to fret openly about a seemingly endless primary campaign and its impact on the party's chances of defeating President Barack Obama in the fall.

In truth, the improving economy has something to do with the nagging concern that plagues some Republicans, with unemployment trending down, consumer confidence up and the Dow Jones Industrial average closing above 13,000 on Tuesday for the first time since before the recession.

Obama couldn't wait to taunt Romney and his Republican rivals in remarks to members of the United Auto Workers union Tuesday.

"You've got folks saying, 'Well, the real problem is, what we really disagreed with was the workers, they all made out like bandits'; that saving the American auto industry was just about paying back unions," Obama said. "Really? Even by the standards of this town, that's a load of you-know-what."

The exit polls in Michigan suggested he may be on to something.

Even in a Republican primary, roughly 4 in 10 voters interviewed as they left their polling places said they supported the government rescue plan for the auto industry.

Little wonder. In Detroit, carmakers and parts companies once fearing extinction added more than 38,000 jobs in 2011, and automakers already have announced plans to add 13,000 more to the payroll this year.

The same survey suggested misgivings among Republicans in the first of the big industrial states to play a role in the nominating campaign. Romney won overwhelmingly, 61 percent to 24 percent for Santorum, among the 1 in 3 primary voters who said what mattered most was backing a candidate able to defeat Obama in the fall.

Yet only 45 percent of those interviewed said they strongly favor the candidate they voted for. Thirty-eight percent admitted to reservations, and 16 percent said they voted the way they did because they disliked the alternatives.

Additionally, the closeness of the Michigan race underscored a deep split between primary voters who described themselves as somewhat conservative, at 31 percent of the electorate, and the 30 percent who said they are very conservative.

Romney won the first, Santorum the second, and by nearly identical margins, additional evidence that the divide that has characterized the nominating campaign since the beginning remains a hardy one.

It will be tested next week in Ohio, Tennessee, Oklahoma and Georgia, Gingrich's political base, and, barring a breakthrough by any contender, later in the month in primaries in Alabama, Mississippi and Louisiana.

As it was, Romney's path to his two-state sweep in Michigan and Arizona on Tuesday was hardly pretty.

Three weeks ago, his aides committed the inexplicable gaffe of permitting Santorum to win caucuses in Minnesota and — especially — Colorado without significant opposition. Romney's narrow win over a winless Paul in the Maine caucuses a few days later only added to the impression of a campaign sputtering as the primary calendar picked up speed.

Santorum quickly rolled to a sizeable lead in the polls in Michigan.

As they did when Gingrich challenged earlier in the winter, Romney and the deep-pocketed super PAC Restore Our Future unleashed an assault on television that quickly narrowed the gap and allowed the former Massachusetts governor to exploit some of Santorum's attention-grabbing statements.

Among them was his observation that Obama is a "snob" for favoring college for anyone who wants to attend. And that reading President John F. Kennedy's 1960 speech about separation of church and state made him want to throw up.

Not that Romney was gaffe-free.

Campaigning in Michigan, where unemployment is 9.3 percent, he blurted out that his wife drives "a couple of Cadillacs."

A day earlier, he seemed to have vivid recollections of a parade that took place in Detroit in 1946, even though he had not yet been born.

Later, in Florida, visiting the site of the Daytona 500 in an evident attempt to establish rapport with auto racing fans, he allowed he was friends with a couple of team owners, but no drivers.