The best course would be to vote for a Congress that will do its job.
Okay, yeah, that one is a long shot.
Looks like waiting for them to die is probably the only real course forward. Of course, that only works if Congress decides to do their job next time. Which also seems unlikely.
My personal evaluation of the situation is that we are all probably fucked. Congress has discovered that it is better to blame each other for the failure than fix the problems. Leading our government to become too dysfunctional to do the basic job of governing itself. From now on it will just get slowly worse until something major happens, then it could go either way.