If McCain is smart, he won't tap Joementum for anything, but rather keep him in the state and block any potential further-left Senator from taking over his empty seat. If for some reason Joe gets voted out, then he can tap him for a position within the Administration.
What's CT's laws on replacing a senator? Rell is Governor and would presumably put a Republican in Lieberman's old seat, unless CT has a similar law to AZ.
That would really be Lieberman's way of saying "fcuk you" to the party that dumped him.
One interesting factor is that the veto-proof Democratic legislature can't really force a bill down Rell's throat requiring that Lieberman's seat be filled by someone in the same party (like Massachusetts did in 2004), since Lieberman technically isn't a Democrat.
