The behavior of the House Republicans seems like madness. But game theory shows that madness can be useful in getting your way. This bodes very badly for the nation.
Look at this thought experiment, attributed by Michael Kinsley to Nobel Prize winner Thomas Schelling.
So you're standing at the edge of a cliff, chained by the ankle to someone else. You'll be released, and one of you will get a large prize, as soon as the other gives in. How do you persuade the other guy to give in, when the only method at your disposal -- threatening to push him off the cliff -- would doom you both?
Answer: You start dancing, closer and closer to the edge. That way, you don't have to convince him that you would do something totally irrational: plunge him and yourself off the cliff. You just have to convince him that you are prepared to take a higher risk than he is of accidentally falling off the cliff. If you can do that, you win. You have done it by using probability to divide a seemingly indivisible threat. And a smaller threat can be more effective than a bigger one. A threat to drag both of you off the cliff is not credible. A threat to take a 60 percent chance of that same thing might be credible.
Dragging our nation off the fiscal cliff would be destructive for everyone. But if the Republicans can make people think that they are crazy enough to do it, they think the Democrats will have to give in.
The problem is made far worse because now that they have committed themselves to this strategy, it will be very difficult for them to not follow through, since failure would make them perceive themselves as losers, and in our current culture being labeled a loser is a fate worse than death. They have probably convinced themselves that the Democrats will give in and they won't have to follow through. But they have backed the Democrats into a corner, where they can't give in without giving the Republican crazies complete control.
Of course, it is psychologically easier for the Republicans to destroy the government, since that have trained themselves to hate it. So they are ok with a stalemate, giving them a tactical advantage.
The psychological need for power and for not losing face may cause huge problems for the country. It is like some Greek tragedy and we can't seem to defeat an evil fate.
The only complete solution to this madness is for the House Republicans to be voted out, as happened in California.