Let’s look at this from ONLY the debate perpective
Who would you rather see debate Obama?
Santorum? (too whiney)
Romney? (too inept- “Okay c’mon I betcha $10,000 the economy is worse now. C’mon you wanna bet?”)
Gingrich? (would be akin to a blood sport)
If Gingrich agreed to VP with Santorum, could Santorum delegate his VP to debate the president? Afterall, it takes more than 1 person to run the administration. I think the public would accept it.