Former Congressman Ron Dellums is a veteran and presumably available (I don’t know the state of his health). That would give Obama a two-fer: first black Secretary of Defense and someone almost as far to the left as himself.
I’m thinking that Bath House would shoot for the moon on the next sec def appointment, as he has no other election to win, and he’d like nothing more than sticking his thumb in the eye of the nation. As such, he could find a black transsexual to fill the spot, and since the USA is into FIRSTS these days, firsts above all else, why not!?