Regarding the government shut-down, the administration and the Republicans are on separate lonely islands, like Gilligan and Crusoe (or Piggy and Jack Shepard). Neither party sees a way to rejoin civilization without egg on its face.
So, the stalemate will continue (and Boehner will live in his red hat) until they start negotiating the debt ceiling. The debt ceiling is the bridge home, egg free.
Spoiler alert! The final chapter of this drama is that the administration will make a small adjustment to the Affordable Care Act that doesn't delay its funding (e.g. a repeal of the medical device tax) in exchange for a comfortable increase in the debt ceiling.
If the markets think otherwise, they're wrong.