It might come as a revelation to many pundits but there is another option for Speaker Boehner. He can look to Democrats for votes. Crazy talk? Only to the Tea Party. Just about everyone else in America believes that Congressional Republicans need to compromise and work with Democrats on a bi-partisan solution.
So Speaker Boehner, with that in mind let me say it again. The votes you need are on the left. They are there for the taking. You can start at a clean-debt bill, which would likely pass. If you desire, you can even add on some spending cuts with no revenue and probably still get it to pass.
What you can't do is craft a bill that relies only on Republican votes. Listen to Kevin Drum: