Are Obama and Boehner stuck in a Nash Equilibrium...again?

It occurred to me that the current train wreck that is carrying out in slow motion in congress this week as the world watches in confusion and horror may have a simple explanation from game theory. This is probably a huge oversimplification but I'll just put it out there.

In game theory two or more opponents have a number of actions they can take and values they can obtain which depend on their own actions and the action of their opponent. A Nash equilibrium occurs when each party knows that the policy they are following cannot be improved given what they know their opponent is doing.

In a sense Obama and Boehner are in such an equilibrium right now but only if they disagree about values are important. If you look at long term values then no action Obama takes will make him better off, they all lead to reduced respect, increased risk for the future etc. Meanwhile, if you look at the short term values only, then Boehner has nothing to gain from acting differently. He'll lose support from the people he needs if he changes his mind. These voters and congressmen are willing to support others who are more extreme or simply not vote at all to get what they want. The respect and acceptance he'd gain would only come from people who don't provide him any benefit such as the media and his opponents.

So I'm saying they are stuck in a Nash equilibrium of sorts, and a pure-strategy one at that, but only because they are playing different games in their heads by disagreeing about whether the short term or long term values are the important ones to take into consideration.

Of course, I'm not the first one to think of this:

Hopefully it's not really a Nash equilibrium and some more thinking will really lead Boehner to a different decision. But it is really is a mixed strategy, that is a random one, then we should all hold on to our seats.