Most commentators think that a clean continuing resolution, based on the budget numbers agreed to last month by Boehner, would pass the House if only put to a vote. See, e.g., Loosinhouse, The Two Words All Democrats Must Start Using Immediately, Daily Kos (Oct. 7, 2013). The shutdown would end, and the government agencies and offices could transition back to doing their work. Congress could then get back to real work instead of the "showdown at the OK Corral" tactics intentionally planned, adopted and pursued relentlessly by the Tea Party wing of the GOP based on the idea that it is okay for a congressional minority to attempt to undo legislative enactments achieved in the ordinary process of legislation by threatening to cause great harm through withholding funds or withholding approval for an increase to the debt ceiling if it (the minority) doesn't get its way.
Boehner, however, says the votes aren't there. And although the radicals have wasted a lot of Congress's time (with endless unsuccessful votes to repeal or defund Obamacare) and a lot of ordinary Americans' time (with furloughed inactivity and the anxiety that non-rich people experience when they aren't getting paychecks but have bills to pay), Boehner claims that he doesn't want to waste time by calling for a vote that will certainly lose. Id.
The Daily Kos (op.cit.) suggests that Boehner shouldn't expect us to believe him when he tells us it simply isn't possible to pass a clean CR because the votes aren't there. There's a list of who would likely vote for funding the government without any strings attached, and it includes a lot of Republicans--enough to pass a clean CR with Democrats. See, e.g., Bendery, Here's a Tally of Which House Republicans Are Ready to Fund the Government, No Strings Attached, HuffingtonPost.com (Oct. 1, 2013, as updated Oct. 8, 2013). That's at least 23 Republicans who, if voting with all 200 House Democrats, would easily surpass the 217 votes needed to pass a clean CR. (The Huffington Post article notes that 4 GOP House members who said they would support a clean CR have now flip-flopped to say they will not.)
And finally other journalists are beginning to ask the kinds of probing questions that makes journalism different from a he-said, she-said echo chamber. Take a listen to this interview by Anderson Cooper of Republican hostage-taker Raul Labrador (R-Idaho): This isn't Fox or MSNBC: You're Getting Real Questions Here (Oct. 7, 2013).
So shouldn't the burden of proof be on Boehner? Why not hold a vote if there is a good chance it could pass? How could it possibly be a waste of time to hold a vote that would end the personal pain and suffering being inflicted on hundreds of thousands of federal employees, their families, their communities, and the economic potential for the country at large?