I would guess the same breakdown, alcoholism, drug abuse, bisexuality, and whatever scenario could be rumored about just about every president. Problem is with Obama, they are more likely factual.
Obama has already execeeded any requirement for getting the boot. This might make Pelosi the VP. Is this even a worse scenario?
If Obama is forced out of office or resigns, Biden will take his place. Biden will then choose a VP -- who I believe is subject to confirmation by the Senate.
Pelosi is practically persona non grata among Democrats right now. There's no way she would be confirmed. But, you can probably guess who Biden would pick -- she already knows the Oval Office well.