It is important to remember that the date we run out of money and would need to borrow more is uncertain. October 17 is the last day on which the government can say with certainty that it can pay all its bills. Money starts to run out at some point after that. General agreement is that a whole bunch of payments due on October 31 and Nov. 1 are impossible to meet without raising the debt limit.
We are also seeing some game playing around what would constitute "default." Conservatives are arguing that a "default" only occurs if we fail to make payments to our creditors (by which I assume they mean bond holders), rather than fail to issue money we owe.
All of which speaks to a conservative wing determined to go past October 17. They may well persuade the GOP centrists that they can continue to hang in past October 17 because "the world won't end" on October 17 (which is apparently the test for the Tea Party faction).
Why hang on? For Boehner, the answer is -- why not? His only alternatives are drive this over the cliff (and thus alienate the Big Business wing of the party) or surrender (which puts his speakership at risk). the longer this drags on, the more they can hope that Democrats will lose their nerve and revert to type and give Republicans something. So we drift on, as Boehner hopes the horse will learn to sing.
It is also possible that the financial interests in the Republican Party will push Boehner to do something before the 17th because no one know what happens psychologically when we cross the line and the U.S. government starts to not pay its bills because it lacks funds. In that case, the most likely play for Boehner is a clean debt limit increase and a clean CR designed to avoid a confrontation until October 2014. That will force the conservatives in his own party to vote for a CR until after election day (as they did in 2012), mitigating the damage Boehner will take for pushing a clean CR and a clean debt ceiling increase.
But we'll see. It's rather uncharted waters here.