Say your wife wants to live in New York and you want to live in California. What to do? Comprimise and live half way in Kansas? No of coures not.
You ALWAYS have to compromise. The key is for both to be able to gain something from it or at the very least live with the compromise. In your example above, if my wife wants to live in New York and I want to live in California we either compromise my desire or hers. If I am the one compromising and we have to live in New York, while I may not be happy with it, perhaps we can work something out where I can live with the compromise.
In the case of politics, I think both sides have dug their feet in on some things which, frankly don't matter in the grand scheme of things. Two months allows the American people to continue for two more months with no tax increase. REGARDLESS of how laughable it is to implement a payroll tax increase in just two months (assuming we get to a stalemate position again), we, the American people, have gotten two more months. For me and my wife, that's roughly $200/month, which could mean the difference in me not being able to pay a bill, put fuel in the truck, or helping my adult daughter who just moved back in with me.
The GOP botched it because their strategy was simply to dig in and demand a 1 year extension at the 11th hour. Really? The Senate had already been dismissed. Did they really think that the Senate would hop back on planes to fly back to DC to negotiate a last minute compromise to extend it to a year?
Additionally, the GOP did include the Keystone rider into the bill to force the Dems (pardon the football terminology) on 4th and long to go for it or punt the ball.
Spin it all you want, there is fault on BOTH SIDES and politics should not be akin to a religious war in that, we cannot compromise. We must stand by our principles, but we continually spin things together to make them something that they are not. The Health Care bill has provisions in it that are unconstitutional, but forcing the insurance companies to do the right thing by not dropping coverage on someone who finds out they have an "expensive" or terminal disease is just the "right thing to do". Those are the principles that should guide us. NOT trying to figure out which political faction or lobbyist will put the most money into our reelection fund.