Here is what Bush should do. Invite Shoooomah, Biden, Layheee, and Feinstein to the White House. Consult with them, take their suggestions. Get some photos taken. Hell, even consult with some more dems. Then go straight out and nominate someone they will hate, but who is imminently confirmable.
It would be hillarious to see them howl about not being consulted, because they were. Instead, they will be howling about not getting to make the pick themselves, which will not sit well with the public.
How many senators did the impeached one meet with before he chose Ruth Buzzy Ginsberg?