The Republican presidential campaign arrives at a potentially pivotal moment Tuesday, with contests in 10 states that should provide the most definitive clues to date about the possible length of the race and whether anybody has a genuine chance of preventing Mitt Romney from winning the GOP nomination.

The coming week offers Romney his best opportunity to begin to break away from his rivals, as he is likely to add — possibly significantly — to the delegate lead he already enjoys. But a popular-vote loss to Rick Santorum in the marquee race in Ohio would once again highlight weakness rather than strength.

The former Massachusetts governor has struggled to gain a significant advantage on his three remaining rivals and has been hurt by his failure to do better against a relatively weak field of candidates.

On Saturday, he got a boost heading into Tuesday by winning the Washington state caucuses. Returns from caucuses in 60 percentof the state’s precincts showed Romney with 37 percent of the vote. Rivals Rick Santorum and Ron Paul battled for second place, while Newt Gingrich ran a distant fourth.

Although there are primaries and caucuses all over the country on Super Tuesday, much of the attention is focused on Ohio, a critical general-election swing state and the most contested of the primaries that day. There, Romney and Santorum are engaged in a rematch of their closely fought battle a week earlier in Michigan.

“Psychologically and politically, Ohio is critical,” Republican strategist Ralph Reed said. “If Santorum wins Ohio, it helps him raise money and extend the game. If Romney wins it, like Michigan, it burnishes the aura of inevitability.”

Whatever the results on Super Tuesday, the Republican race probably will continue for many weeks, if only because party rules make it difficult for any candidate to quickly amass the necessary 1,144 delegates to clinch the nomination. Those rules and the existence of super PACs backing individual candidates have diminished the incentive for losing candidates to quit the race.

By historical standards, this week’s balloting pales in comparison with Super Tuesdays of the past. Four years ago, there were roughly two dozen contests on Super Tuesday. But with 437 delegates at stake in 10 states, and the beginning of delegate awards in an 11th, Tuesday marks the biggest single day of voting in the 2012 Republican race.

Sweep unlikely

Taken together, Tuesday’s contests provide a rich mixture of regional and demographic constituencies that make it unlikely that any candidate can hope for a sweep, which means everyone has something important at stake.

Romney needs to emerge as the overall winner if he hopes to prove he is the genuine front-runner. Santorum, the former senator from Pennsylvania, wants to show that the GOP race is a two-person contest and that he has the political appeal to win. Former House speaker Newt Gingrich needs a victory in Georgia to justify continuing his candidacy. Paul needs a breakthrough that has eluded him all year.

At the beginning of last week, Santorum held a clear lead in Ohio, but that was before Romney won Michigan and Arizona. Since then, Romney has gained ground, just as he did on his way to his narrow victory in Michigan. A Quinnipiac University poll released Friday showed Santorum leading Romney in Ohio, 35 percent to 31 percent.

But the vote total in Ohio is only part of the story, as the race becomes a battle to accumulate delegates. Even if he wins the popular vote, Santorum could easily lose the delegate battle. The Romney campaign said Saturday that Santorum has not qualified for 18 of the possible delegates up for grabs.

Santorum is now facing the consequences of having to run a shoestring campaign for most of the past year, when few people took seriously his ability to challenge Romney. Although he has been able to raise considerable money since winning three states on Feb. 7, he has been slow to develop the political infrastructure needed for a long nomination contest.

Beyond Ohio, he will feel the pinch even more Tuesday in Virginia, where both he and Gingrich failed to qualify for the ballot. That leaves Paul as Romney’s only challenger in the state. As a result, Romney could win all 46 delegates at stake if he takes each of the congressional districts and a majority of the popular vote statewide.

Santorum has keyed on two Southern states, Tennessee and Oklahoma, where he will count on support from evangelical Christians and tea party activists to carry him to victory. Gingrich has made Georgia, which he represented in the House, a must-win state for his campaign, and while he is favored there, Santorum and Romney are looking to win delegates in the state.

The other Super Tuesday states are Massachusetts, Vermont, Alaska, Idaho and North Dakota. Wyoming will start awarding some delegates from its caucuses Tuesday but will not conclude that process until later in the week.

Delegates vs. states

Terry Nelson, a Republican strategist, said there are two main measures that will be used to determine who wins on Super Tuesday: delegates won and states won.

“One measurement, and given the nature of the race the one that matters the most, is who wins the largest number of delegates,” he said. The race “seems to be more in the category of a long-term delegate fight, so the person who comes out on top of that is going to be the person best positioned to win the nomination. But it’s politics, and it’s about expectations in individual states. The candidates’ performance in those states will have an impact in judging perceptions as to the winner.”

Romney can add to his delegate haul if he wins Massachusetts, where he served one term as governor; Virginia; Vermont; and Idaho, where he got an enthusiastic reception during a campaign rally last week. But he expects to pick up delegates in states that Santorum or Gingrich are favored to win, thanks to the rules that govern GOP contests this month.

In Tennessee, for example, a candidate must win more than 66 percent of the vote to pick up all the delegates awarded in each congressional district. A second-place finisher who captures more than 15 percent of the vote gets one of the three delegates in those districts.

In Oklahoma, the only way a candidate wins all the delegates in a congressional district is by winning a majority of the vote — which is not easy in a four-person race. Otherwise, the candidates are divided evenly among the top three finishers, assuming all three cross the 15 percent threshold.

Georgia may be Gingrich territory, but Romney’s team has targeted congressional districts in the Atlanta metropolitan area.

Any candidate who wins a state Tuesday will try to claim some of the bragging rights. If Romney were to win a majority of the states, including Ohio, his campaign probably would argue that it is time for the others to begin to step aside so that the Republican Party can get ready for the general election campaign against President Obama.

On the other hand, said Republican pollster Whit Ayres, if Santorum wins Ohio, “I don’t know that he has to win a whole lot of other states to keep it going.”

And if Romney wins Ohio, Gingrich wins Georgia and Santorum wins Tennessee and Oklahoma? “Then they pack it up and go fight again,” Ayres said. “Then it becomes what a bunch of people have written about — a long delegate slog.”

Staff writer Aaron Blake contributed to this report.