Also, I do not see Obama as having too much to lose by taking her.
He has much to lose. She has too big of a personality to play #2. Heck, she poked her nose into too many things when Billy BJ was POTUS.
Plus, having her on the ticket means the repubs can replay anything and everything nasty her campaign said about him. That’s a big old flaming tire around the head that he will have to wear.