I suspect he has been asked by Trump to hang on because if he resigns, I’d highly doubt any Trump appointee can get through the Senate, thereby leaving Rosenstein, the #2, to be the acting Attorney General. I also doubt Rosenstein can be fired for political reasons, although he certainly has earned it in spades. The long & short is that Trump is in a public relations political trap with Sessions.
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“You can vote your way into socialism, but you have to shoot your way out.” — Too fundamental to have an attribution