absolutely nothing.
First off, there is a giant downside to talking about McCain's VP pick, it replaces the conversation over who will make the better president. And the McCain vs Obama discussion is a contest that Obama will win. Equally important, people are not going to decide based on the VPs, but on the presidential candidates.
Second, she appears to be a walking disaster. Letting her self destruct will be much more damaging to McCain that having the Dems be an instigator of it. When she does it all by herself it makes it completely apparent that she, and she alone, is the cause of her problems.
Third, the news media smells blood and an ongoing set of very interesting stories in her. They are going to tear into her a lot, even if the campaign doesn't do anything. And many independent groups will also do so.
The one thing the Obama campaign should do is get people to view this selection as a measure of McCain's judgment. Don't make too big a deal out of it - but try to make that connection now before she blows up, when the McCain campaign will go along with this measure.
Sarah Palin is her own worst enemy. When your opponent is going to keep hurting themselves, stay out of their way and let nature run it's course.