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Mr. Santorum, perhaps in a nod to the recent swing in the polls, was more cautious as he spoke to voters in Lansing.

“I think the fact that we are doing as well as we are is a pretty big deal in this state,” he said.

Mr. Paul ended a three-state tour in Michigan on Monday. He planned to await Tuesday’s outcome in Virginia. Mr. Gingrich spent Tuesday campaigning in his home state of Georgia.

No matter the top finisher, Mr. Romney and Mr. Santorum stand to split the 30 delegates at stake in Michigan because the state distributes delegates proportionally. By contrast, Mr. Romney is favored to win all 29 delegates in Arizona, which features a winner-takes-all system.

So far, Mr. Romney has 123 delegates to 72 for Mr. Santorum. Mr. Gingrich has 32 and Mr. Paul has 19, based on an Associated Press count. It will take 1,144 delegates to win the party nomination at the Republican National Convention in Tampa, Fla., this summer.