Probably Obama's game is get Bush to sign off on something he wants and if things go wrong, he can pawn the blame on Bush. Obama wants to credibly blame the previous administration as long as he can.
That's my guess too. Obama is essentially a coward. Getting Bush to do the Auto bailout for him is just his way of voting "present" one last time.
After Bush is gone, the congress will take blame for all things bad. That will be fun to watch!