Starting with the Michigan and Arizona primaries on Tuesday, Republican front-runners Mitt Romney and Rick Santorum will face each other in a series of one-on-one matchups that are likely to determine the direction of the rest of the race for their party’s presidential nomination.

Next week and then in a handful of contests the following week on Super Tuesday, Romney will have a chance to show that he can defeat a concerted conservative challenge and solidify his claim that he is the GOP’s inevitable nominee. So far, he has had a mixed record in winning over the most conservative elements of the party, but he has been able to win in states where those voters have splintered their support among multiple candidates.

The upcoming contests are expected to draw only limited engagement from the other remaining candidates, former House speaker Newt Gingrich (Ga.) and Rep.Ron Paul (Tex.).

The contests offer Santorum, a former senator from Pennsylvania, a chance to prove what he and other conservatives have long claimed: that a moderate such as Romney cannot beat one of them in a head-to-head matchup. His supporters point to Santorum’s sweep of three contests on Feb. 7, which has propelled his surge since.

“Next Tuesday’s election is pivotal for Mitt Romney,” said GOP consultant Mike Dennehy. “Michigan is really the battleground for the future of the nomination.”

Paul will also get a clean matchup with Romney on Super Tuesday in Virginia, where only those two candidates met the stringent qualifications for a place on the ballot.

The coming calendar poses the biggest problem for Gingrich, a onetime conservative alternative to Romney who has dropped in the polls and has not been able to raise enough money to run a national campaign.

Gingrich is largely looking past the contests in Arizona and Michigan, and in Washington state on March 3, and is instead focusing on Super Tuesday races in Ohio, Oklahoma, Tennessee and Georgia, his home state. He will find competition in all of them from Santorum and Romney.

GOP pollster Jon McHenry said two of those races appear to be particularly significant.

“Ohio and Georgia strike me as the most important Super Tuesday states,” McHenry said. “They’re large states; one is a Deep South, appeal-to-the-base state, and the other is the quintessential swing state. And the timing means you can’t just camp out there and win by showing up.”

Romney has been building organizations in all the Super Tuesday states, announcing slates of elected officials, key party activists and local business leaders who are backing him, and he hopes to take advantage of their political networks on the ground. He will also probably have a money advantage, as his campaign and a super PAC supporting him are vastly outspending his opponents. This could be particularly critical at a time when TV ads will take on an even greater role.

Although his opponents may point to individual states and moments in the race as evidence of Romney’s vulnerability, his campaign hopes its all-around performance will erase any doubt that he is the front-runner.

“It’s no longer possible to focus all your energies on a single state and mobilize a small core group to show well in that state,” GOP consultant Fred Malek said. “Rather, it requires a broader appeal, and I predict Romney wins big over next two weeks.”

Meanwhile, Romney’s opponents, who are not as well-funded, will have to pick their spots, both on the air and on the ground.

Over the past several days, Santorum has made campaign stops in Washington, Michigan, Idaho, North Dakota, Oklahoma, Ohio and, on Sunday, Georgia. He spent Tuesday in Arizona, and his campaign is airing ads in Arizona, Ohio, Georgia, Oklahoma and Tennessee.

Santorum’s advisers said his schedule is a reflection of his rising poll numbers and fundraising efforts, both of which would probably accelerate with another win before Super Tuesday.

“We’ve been in Washington. We’ve been in Idaho,” Santorum spokesman Hogan Gidley said. “We’re running a national campaign.”

But, he added, “in general, states where the Republican electorate is more moderate are less good for us, and states where the electorate is more conservative are good for us.”

About the only states not on Santorum’s radar are the two Northeastern Super Tuesday states, Massachusetts and Vermont. Romney, as a former governor of Massachusetts, is a heavy favorite in both.

Gingrich’s campaign, meanwhile, has shown that it will focus on Super Tuesday — Georgia in particular but also other Southern states — and will largely skip the preceding contests in Arizona, Michigan and Washington. Gingrich has done well in the South so far, winning the South Carolina primary and performing strongly in the Florida panhandle.

He began a two-day swing through Georgia on Friday and visited Oklahoma on Monday. He will return to Georgia after a debate in Arizona on Wednesday and may spend Feb. 28 in his home state rather than in Arizona or Michigan.

During an appearance last week in California, whose primary is not till June, Gingrich said he wouldn’t dismiss Michigan entirely, largely because of the rules there governing how delegates will be awarded. Even a modest showing in the polls would give him some delegates.

By largely skipping the pre-Super Tuesday states, though, Gingrich may allow Santorum to enter Super Tuesday as the consensus alternative to Romney.

“Gingrich can’t allow this to continue and still raise money to pay for coffee — much less a campaign,” GOP strategist Dan Hazelwood said.

Asked in Los Angeles last week whether he has miscalculated by ignoring the pre-Super Tuesday states, Gingrich demurred.

“This thing has had a wild rhythm; it resembles riding Space Mountain at Disney,” he said. “I’ve been the front-runner twice; I suspect I will be a front-runner again.”

Staff writers Philip Rucker, Amy Gardner and Rosalind S. Helderman contributed to this report.