For the Supreme Court seat.....why not offer it to Sessions (the former Alabama Senator, and current Attorney General)?
First, he's already sat through the 'got-you' situations with the Senate and would easily be accepted by the Senate.
Second, it gets rid of him as the Attorney General, where he's been a 'loser', and you could bring in someone who'd change the dynamics of the Attorney General's office.
Odds of this happening? One in a billion.