I recommend Stan Collender's pessimistic column about budget politics next year, but it gets me thinking again about what a difficult position the Republican conference is going to be in during the 112th Congress if they at least win the House.
It seems to me that Republicans could have three basic strategies. One, working and compromising with the president to try to get as much of their agenda passed as possible, is presumably not even a plausible response for this batch of Republicans -- I assume everyone agrees on that, right? Note that they basically did adopt that strategy (except for impeachment) in 1997-2000, but no, I don't think we'll see it.
The second strategy would be to go on offense: to try to get their agenda passed by streamrolling Barack Obama and the Democrats. In other words, to imitate 1995. The problem with this one is that it would be spectacularly unsuccessful, and those who remember 1995 know it. Surely that includes John Boehner, who is almost certainly no fan of Newt Gingrich. Depending on the size of their majority, it's not even clear that Republicans could agree on a budget on the floor of the House. Even worse for them, if they can pass a Tea Party budget, it will almost certainly be stopped in Senate (best-case scenario 51 Republicans including Olympia Snowe and Susan Collins aren't going to try to shut down the Department of Education). And in the highly unlikely chance that they do get agreement on a budget that could make the conservative base happy, they'll never get enacting legislation through WH vetoes. The whole exercise would leave few if any substantive accomplishments, and plenty of ugly votes for the Democrats to sift through for the 2012 campaign. Even worse, a veto fight produced by this strategy would yield a government shutdown, which might thrill Tea Partiers but would likely help Obama and produce Boehner-destroying chaos inside the Republican conference.
The third strategy would be to forget about their agenda, and basically pretend they're still in opposition -- that is, to continue rejectionism. Don't think 1995, or 1997-2000, but think more of 1993-1994. Obviously, this works best if they don't actually take control of either House of Congress, or at the very least fall short in the Senate. Still, they certainly could try it even if they have majorities in Congress. They could (as Democrats did this year) not bother with a budget. They would have to pass appropriations bills, but instead of using that process to really challenge the status quo, they would win some symbolic stuff, and fight carefully chosen fights on specific issues. So they could actually eliminate earmarks and make a big show about including a statement of Constitutional legitimacy in all the bills they pass, giving them some victories to take home, and they could stage some losing votes on Tea Party priorities, preferably Constitutional amendments that they could all vote for without risking much. Then, they could pass most of the appropriations bills without major veto-bait, but go ahead and maybe zero out some ACA funding and have a major fight over that one before surrendering, without the threat of a government shutdown hanging over everything. Oh, and they could schedule votes all day long on cap-and-trade, and Obama's budget, and try to get Dems to take bad votes on them -- while fighting real fights over in the Senate on judicial and exec branch nominations.
Of course, each of these options would be accompanied by lots of investigations into Obama administration scandals (although actually going through with impeaching the president seems highly unlikely in the 112th Congress).
As I think you can tell, my guess is that Boehner would prefer option #3. The question is whether he could get away with it without drawing the wrath of GOP activists, since it involves basically surrendering most of the non-symbolic GOP agenda without really fighting (and losing) for it. I don't know the answer to that. We do know that a whole lot of Republican Members of Congress are going to be paranoid about primary challenges, but how that plays out will depend on lots of things, beginning with just how many seats they actually hold after November.