The Republicans seem to be caught in a time warp. They think it is 1981 and all that's needed is tax cuts in order to solve any problem. They see Obama's popularity and seem to think he is Ronald Reagan. Wishful thinking.
Obama is just going to have to govern without them. Humor them, treat them gently and with respect, but otherwise just ignore them, except to defeat them one by one in elections.
And God help us if they take power again anytime soon. They need to wander in the wilderness for at least 40 years.