I was thinking about this last night. Right before a coach is fired, he gets a vote of confidence from the athletic director. Then, the next day the coach resigns (read fired) to spend more time with his family. So when I saw last night that Geithner said the President asked him to stay. I assumed his goose was cooked. But then I thought, who would Obama pick to replace him and that train of thought led me to believe that Geithner's not going anywhere.
Okay, follow my reasoning. If Geithner goes, who could Obama possibly choose that would make it through the senate? Obama clearly is an arrogant ideologue, and his ego would not allow him to pick anyone who wasn't at least as socialist/Keynesian as him (Note: I am not saying that all those who follow Keynes' economics are socialists). But after the rating meltdown, I think even the Democrats in the senate might want someone with a little more supply side philosophy. And Obama can't have that; it would be an admission that his policies were wrong for the last 25 months. The President could wait and make a recess appointment in December, but that would be too late to help his re-election.
So Obama's in a pickle both politically and ideologically. If he sacks Geithner's his replacement will almost certainly have to be move to the right to get confirmed by the senate. I think Obama will take the political heat and keep Geithner so the two of them can get on with QE3 and 'investing' money we don't have. Way to put America first champ.