“Well, I’d like to see Gen. Petraeus warm up,” Dole said. “I don’t know anything about his politics, whether he has an interest. It’s kind of a time for another Eisenhower, in my view.”

This isn’t the first time the popular general’s name has been floated as a possible GOP savior — and it won’t be the last. Petraeus has political impulses but hasn’t revealed if they are conservative ones, and he might not even be a Republican.

The CFR’s Senor is skeptical, even though Petraeus would be an appealing candidate. “He has to be focused like a laser beam on Afghanistan,” Senor said. “If he is as successful in Afghanistan as he was in Iraq, nothing else matters, and he will instantly be considered a top-tier candidate for president.

“But in order to be successful, he has to work very closely and effectively inside this administration, and very loyally to the commander-in-chief. He’s going to work successfully with this administration, and then all of a sudden announce that he’s stepping down to run against the commander in chief under which he served? As a practical matter, that’s unlikely.”