BOEHNER EYES BLUE DOGS FOR BUDGET DEAL…. House Speaker John Boehner (R-Ohio) has struggled for several weeks with an arithmetical problem. He could strike a budget deal that would make his own extremely conservative caucus happy, or he could strike a deal that the Senate and White House would find acceptable.

But he couldn’t do both. If the Speaker went with the former, and stuck to his guns on a right-wing plan that the American mainstream would find offensive, the base would be happy but a government shutdown would be unavoidable. If Boehner went with the latter, he’d lose much of his own caucus, and would (again) need House Democrats to finalize a deal.

As of yesterday, Paul Kane reports that the Speaker is at least open to Door #2.

Having difficulty finding consensus within their own ranks, House Republican leaders have begun courting moderate Democrats on several key fiscal issues, including a deal to avoid a government shutdown at the end of next week.

The basic outline would involve more than $30 billion in cuts for the 2011 spending package, well short of the $61 billion initially demanded by freshman Republicans and other conservatives, according to senior aides in both parties. Such a deal probably would be acceptable to Senate leaders and President Obama as long as the House didn’t impose funding restrictions on certain social and regulatory programs supported by Democrats, Senate and administration aides said.

The fact that Republican leaders have initiated talks with some Democrats shows some division within House Republicans just two months after taking over the House.

Ya think?

Ideally, John Boehner would 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.

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. 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.”

Which is where “centrist” and Blue Dog Democrats come into the picture. Boehner figures he might be able to thread the needle, crafting a deal the Senate and White House can live with, and get to 218 in the House with a coalition of center-right Dems and sane Republicans.

That would prevent a shutdown and lay the groundwork for future talks. It would also cause widespread apoplexy among conservative activists and the GOP’s Tea Party base, and perhaps even put Boehner’s role as Speaker in jeopardy.

Indeed, perhaps the only development yesterday that was as interesting as outreach to the Blue Dog Dems was House Majority Leader Eric Cantor (R-Va.) noticeably putting some distance between his budget approach and Boehner’s. In fact, Cantor suggested he isn’t even in the loop when it comes to where things stand, telling reporters, “There is a difference in my knowledge base.”

Insert joke here.

If or when push comes to shove, and Boehner feels the need to strike a deal that the hysterical wing of his party won’t like, will Cantor have the Speaker’s back or will Cantor stab the Speaker in the back?

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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.