“If no one is an immediate front-runner,” Mr. DeMint said, “I think you might see a whole new cast of Republican candidates out within the next couple of months.”

He declined to say whom he would like to enter the race, but he praised the work of new Republican governors, particularly Gov. Chris Christie of New Jersey. (Mr. Christie has repeatedly said he has no interest in running, but has boasted that he would fare well if he did.)

“I’m not going to mention any more names,” Mr. DeMint said in an interview here. “But I think there are a lot of names out there bubbling around, particularly governors who have realized that doing basic common-sense things tend to inspire Americans today.”