Mr. Bauer believes that if Mr. Pence ran, he would quickly build support among socially conservative voters. “The nomination battle would be very wide open without Mike,” Mr. Bauer says, who is one of several activists urging Mr. Pence to join the nomination fight…

The Indiana lawmaker, who first won election to Congress in 2000, also has the backing of budget hawks such as Chris Chocola, a former Indiana congressman who is now president of the fiscally conservative Club for Growth. “Mike has the retail appeal of Huckabee but is an across-the-board conservative with all the credentials. There is no one else like that,” says Mr. Chocola.

Feeding speculation about his presidential ambitions, Mr. Pence has visited Iowa, New Hampshire and South Carolina in the past year, all states with early roles in the nominating process. And yet Mr. Pence and others in his camp continue to drop hints that he’s shying from a White House run. The thought of a presidential campaign, Mr. Pence said in an interview, “is more humbling than tempting.”He says he’s weary of Washington. “I prefer the Flat Rock River to the Potomac River, and the Flat Rock is about a half a block from my house,” he said.

Associates in Indiana say the governor’s race fits him best, and would position him for a potential future shot at the White House. James Garfield, 130 years ago, was the only man ever elected president straight from a House seat.