If I were the Obama campaign director I'd dish out any anti-Gingrich propaganda I had previously saved up, now.
Why would the Obama campaign want to put him back in the headlines and make Republicans feel defensive about Gingrich?
It will all be "unofficial" of course, through an officially independent conservative PAC with no website, no public profile, and no press releases. I'd highlight how Gingrich is just a crass opportunist like Romney, and that he's "not the proper conservative". The goal is to shift half of remaining Gingrich supporters to Santorum to overcome Romney's money bags.