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Rep. Ron Paul, Texas Republican, who had yet to win a contest, spent his time in the run-up to Tuesday concentrating on caucuses in Idaho, North Dakota and Alaska, where his campaign said thousands of people turned out to see him at events over the past week.

“The momentum is building,” Mr. Paul said at his postelection party in Fargo, N.D.

Mr. Gingrich had focused his efforts on Tennessee and Georgia, saying he needed to win the state he represented for years in Congress if his campaign was to remain viable.

Even though he placed third in Tennessee, Mr. Gingrich said at a party in Atlanta on Tuesday that his victory in Georgia keeps him alive, and he deemed himself “the tortoise” in the race.

“I hope the analysts in Washington and New York who spent June and July explaining our campaign was dead will watch this tonight and learn a little bit from this crowd,” Mr. Gingrich said.

Mr. Romney and Mr. Santorum fought chiefly over Ohio, where they hit on similar themes of smaller government, lower taxes and a stronger military — and calling for the repeal of Mr. Obama’s health care law, approval of the Keystone XL pipeline project and a tougher stance on Iran.

They also worked to draw distinctions with each other.

Mr. Romney painted Mr. Santorum as a Washington insider, while he billed himself as a turnaround artist, telling audiences that his 25 years in business, his work to revive the 2002 Winter Olympics and his experience as governor of Massachusetts equipped him with the knowledge needed to address the nation’s economic and unemployment woes.

Mr. Santorum argued that Mr. Romney’s support of universal health care in Massachusetts would hurt the party’s chances of defeating Mr. Obama in November, and he accused the former governor of trying to cover up past support for the same sort of federal health care mandate that he now rails against on the campaign trail.

The former senator also played up his blue-collar, western Pennsylvania roots, telling audiences that he understands them, while arguing that the party must work to breathe new life into the small towns that embody the family values that social conservatives hold dear.

The outcomes of the 10 contests on Super Tuesday were not expected to be as decisive as the big day in 2008, when Sen. John McCain of Arizona essentially sewed up the nomination.

But Tuesday was expected to bring some clarity to the grind-it-out race, and to go a long way toward answering whether Mr. Romney could break away from the rest of the Republican presidential pack and persuade voters that he gives the party the best chance of defeating Mr. Obama in the November election.

Mr. Romney had been riding a winning streak, with recent wins in Maine, Arizona, Michigan, Wyoming and Washington state.

He also received a boost over the weekend when House Majority Leader Eric Cantor of Virginia announced his backing.

But his high-profile endorsements have not proved to be decisive — and Mr. Santorum, Mr. Gingrich and Mr. Paul all have campaigned against the “elites” in Washington that they say are dragging the party and the country in the wrong direction.

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