TOLEDO, Ohio >> A relieved-sounding Mitt Romney is hoping 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 an upset, rival Rick Santorum faces stiffer competition for conservative votes when the contest moves into Newt Gingrich territory.

Gingrich, the former U.S. House speaker from Georgia, sat out Arizona and Michigan and is counting on Southern states voting Tuesday to revive his up-and-down campaign. Texas Rep. Ron Paul could also be a factor in Tuesday’s delegate count, especially in caucus states such as North Dakota.

Romney’s slim victory in his native Michigan — 41 percent to Santorum’s 38 percent — raised questions about whether a shift in strategy is needed. He acknowledged making 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 boasted Wednesday that he was walking away with half of Michigan’s delegates after coming close to winning what originally looked to be a Romney stronghold.

"We’re feeling very good that we sustained ourselves and withstood the attacks, and we think we’re going to have a very, very good Super Tuesday," Santorum said on Bill Bennett’s syndicated radio show.

The former Pennsylvania senator is focusing on three big prizes among the 10 Super Tuesday states: Ohio, Oklahoma and Tennessee.

Washington state’s caucuses are first, on Saturday. Three days later comes Super Tuesday, with 419 delegates up for grabs. The contests also include Alaska, Georgia, Idaho, Massachusetts, Vermont and Virginia.

All four campaigns face financial strain: 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 was campaigning Wednesday in Ohio before heading to North Dakota. Santorum planned events in Tennessee.

Gingrich was campaigning 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 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 struggle to pick a nominee has coincided with a rise in Obama’s prospects for a second 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.

Unopposed for the Democratic nomination, Obama timed a campaign-style appearance before United Auto Workers Union members in Washington, D.C., for the same day as the Michigan primary. Attacking Republicans, he said assertions that union members profited from a taxpayer-paid rescue of the auto industry in 2008 are a "load of you know what."

All the Republicans running for the White House opposed the bailout, but in the auto state of Michigan a survey of voters leaving polling places showed about 4 in 10 supported it.

Michigan loomed as a key test for Romney as he struggled to reclaim his early standing as front-runner in the race. Santorum rolled into the state on the strength of surprising victories on Feb. 7 in caucuses in Minnesota and Colorado and a nonbinding primary in Missouri.