TOLEDO, Ohio

A relieved-sounding Mitt Romney hopes to parlay twin victories in Arizona and Michigan into Super Tuesday momentum as the GOP presidential race sweeps across 10 states at once next week. After falling short of a Michigan upset, rival Rick Santorum faces stiffer competition for the conservative vote as he moves into Newt Gingrich territory.

Gingrich, the former U.S. House speaker from Georgia, is counting on Tuesday’s Southern primaries to revive his campaign. Texas Rep. Ron Paul is also a factor, attempting to mine delegates next week in caucus states like North Dakota.

Washington state’s caucuses are first, on Saturday. Three days later comes Super Tuesday, with 419 delegates at stake, including big primaries in Ohio and Georgia.

Romney’s slim victory in his native Michigan — 41 percent to Santorum’s 38 percent — raised questions about whether he needs to shift strategy. He acknowledged making personal mistakes and said he was trying to “do better and work harder.”

“We didn’t win by a lot, but we won by enough,” the former Massachusetts governor told cheering supporters in Michigan, where his father was governor in the 1960s.

Santorum vowed to stay the conservative course he has set. “A month ago they didn’t know who we are, but they do now,” he told his supporters.

All four candidates face financial strains as they try to advertise in a series of states expensive for campaigns. It would cost about $5 million to run a week’s worth of heavy ads across all the states that vote Tuesday.

Romney signaled that he intends to stick to his core campaign message of fixing the economy and reducing unemployment in a nation still recovering from the worst recession in decades.

“More jobs, less debt and smaller government — you’re going to hear that” over and over in the states ahead, he said Tuesday night.

Despite the close race in Michigan, Romney powered to an easy victory in Arizona, and the combined effect is precious momentum over Santorum in the most turbulent Republican presidential race in a generation. Romney tweeted his delight: “I take great pride in my Michigan roots, and am humbled to have received so much support here these past few weeks.”

The Super Tuesday races could go a long way toward determining which Republican will take on Democratic President Barack Obama this fall.

Romney will campaign today in Ohio before he flies to North Dakota. Santorum was already campaigning in Ohio when the verdict came in from Michigan.

Gingrich and Paul made little effort in Michigan or Arizona, pointing instead to next week’s collection of contests in all corners of the country.

Gingrich is campaigning today in Georgia, the state he represented in the House for 20 years. Contests there and in Tennessee give him an opportunity to breathe some life back into his bid. He won in South Carolina but struggled in Florida.

Romney’s Arizona triumph came in a race that was scarcely contested, and he pocketed all of the 29 Republican National Convention delegates at stake in the winner-take-all state. He won by 47 percent to Santorum’s 27 percent.

Michigan’s primary was as different as it could be — a hard- fought and expensive contest that Romney could ill afford to lose and Santorum made every effort to win.

In Michigan, 30 delegates were apportioned according to the popular vote. Two were set aside for the winner of each of the state’s 14 congressional districts. The remaining two delegates were likely to be divided between the top finishers in the statewide vote.

With his victory in Arizona, Romney had 163 delegates, according to the Associated Press count, compared with 83 for Santorum, 32 for Gingrich and 19 for Paul. It takes 1,144 to win the nomination at the convention in Tampa this summer.

The lengthening GOP nomination struggle has coincided with a rise in Obama’s prospects for a new term. A survey released Tuesday shows consumer confidence at the highest level in a year, and other polls show an increase in Americans saying they believe the country is on the right track.

Along with the improving economy, the long and increasingly harsh campaign, in which Gingrich and Santorum have challenged Romney as insufficiently conservative, has prompted some GOP officials to express concern about the party’s chances of defeating Obama.