THE NUMBER THAT MATTERS TO BOEHNER IS 218, NOT $33 BILLION…. With just one week to go before an inflexible shutdown deadline, there was reason for optimism late Wednesday. Vice President Biden, directly involved in budget negotiations, suggested there’d been a breakthrough. “We’re all working off the same number now,” Biden told reporters.

Perhaps “all” was the wrong word.

Yesterday, Capitol Hill was abuzz with discussion about the $33 billion target for cuts, which would be the single largest, one-time reduction in American history, despite the struggling economy. But if House Speaker John Boehner (R-Ohio) hoped for positive feedback from his caucus Thursday, he was probably disappointed.

As House Republican leaders worked to cobble together a spending plan for this year that can win bipartisan support, their more conservative members made increasingly clear on Thursday that they consider a proposed $33 billion budget cut to be insufficient.

Even as Speaker John A. Boehner urged Republicans to keep in mind that they would have additional opportunities in the coming weeks to cut long-term spending, some members of his caucus said they would be willing to accept a government shutdown if necessary to back up their demand for $61 billion in cuts for the current fiscal year. […]

The immediate question, though, remained whether Mr. Boehner could bring House Republicans along on a deal for a $33 billion cut. “If that’s the number, it ain’t good enough,” said Representative Jason Chaffetz, Republican of [Utah].

For House GOP leaders, the key number right now isn’t $33 billion, it’s 218 — the number of votes a measure needs to pass the chamber. Boehner is relatively close to reaching some sort of deal with Democrats that he can live with, but the question is whether he can get his caucus to live with it, too.

Reiterating a point from earlier in the week, Boehner would much prefer to be a strong House Speaker with resilient credibility among his own members. He could negotiate with Democrats, go to his caucus and assure them he reached the best possible deal, and they’d believe him and vote accordingly. Boehner is, after all, their Speaker — the most powerful Republican in America.

But that’s not the case. Boehner is a weak Speaker, leading a caucus that doesn’t necessarily trust him, dominated by freshmen who don’t really know him and owe no allegiance to him, and filled with boisterous extremists who’d rather destroy than deal. The Speaker could work something out with the Senate and White House, explain to House Republicans it’s the best deal possible under the circumstances, only to hear from his own members, “No, you’re wrong, this isn’t good enough.”

For the record, the House Republican majority has 241 members. Boehner, if he manages to strike a deal with Democrats, which is by no means certain, could lose no more than 23 members of his own caucus before having to rely on Democrats to pass the deal.

Does the hysterical wing of the House GOP have more than 23 members? You bet it does — and Boehner knows it.

The Speaker may think that gives him some added leverage in the talks. He can go to Dems and say, “You guys don’t understand; my caucus is nuts. You have to give me more or the thing can’t pass.” Democrats won’t find this especially compelling. Call it a hunch.

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Follow Steve on Twitter @stevebenen. Steve Benen is a producer at MSNBC's The Rachel Maddow Show. He was the principal contributor to the Washington Monthly's Political Animal blog from August 2008 until January 2012.