To anyone paying attention, Boehner's problem is simple. He knows allowing his party to shut down government would be political suicide for him and his party. The problem is the Tea Party doesn't see it this way. To them, less government is always better. Full Stop. No ifs, ands or buts. Government shutdown? To the Tea Party, that may be even better than defunding Obamacare and savagely cutting the rest of the non-defense budget.
The only way for Boehner to not allow his party to shut down government is to work with the Democrats. Of course that's political suicide for a Republican but it's the only way to prevent his party from committing its own political suicide. No matter what tricks he tries to play, it's going to be obvious that it's his party that is intent on shutting down government. The only question is when does he come to this realization? Before or after he's let the country and his party go off a cliff?