Since it appears voters will put the GOP in the driver's seat this year, the question remains: what do Republicans want? Of course, they've put out their 'pledge', but that is boring, frankly. What do the Republicans on this board want the next Congress to do, assuming that it is Republican? What do they want Obama to do, assuming he were shocked enough by the election to work with the next Congress?
The thread has gotten off course onto guesses about what the GOP members of Congress want. I'll put my two cents in on the narrower form of the question at hand.
I think everyone of both parties want to see more jobs as a sign of recovery from the Great Recession. The Republicans want to see the scales tip more to the side of private sector job creation rather than a reliance on direct public sector job creation. To Republicans that means easing government burdens on those who produce jobs, thus the goals of extending the tax cuts and redoing health care. Republicans don't expect the President to wholeheartedly agree with their desired direction. I think they want the President to move to the middle much as Clinton did with programs such as welfare reform.