If he doesn't step down, he gives the Democrats a license to filibuster anything and everything, and allows them to NOT look petty and partisan while doing so. Essentially, he's just killed the entire GOP agenda for two years if he stays on.
I don't think his resignation is needed--just a swift, peremptory, SILENT removal from the leadership post.
Second, Bush can benefit from a weakened Lott to take the arrows for him.
Sorry, Bush would end up being in the position of taking arrows that are rightfully Lott's.