I see this as Boehner is bluffing, and Barry knows it.
Boehner wouldn't cut off funding for military operations in Libya, because the Dems would make political hay with that. Dems would paint Boehner as cutting off ALL the troops from ALL funding and the Repubs would not only look like fools, it would cost them in the election next year.
I say these things because Boehner does NOT articulate a clear, unbridled message.
Barry will continue to obfuscate and spin and otherwise keep Boehner guessing.
The business with increasing the debt ceiling and how Boehner blinked is all the precedent I need to see.