Greg asked earlier, “Do House Democrats have any leverage in the debt talks?” Barack Obama’s quick statement today to reporters made it clear that: yes, they do.

By emphasizing that “Democrats and Republicans are going to be required in both chambers,” the president inched towards defining a standard under which any grand bargain will require majorities of both parties in both Houses of Congress.

In reality, Obama was basically acknowledging the mathematics and politics of the situation. We know that at least 50 of the 240 House Republicans, and probably a good deal more, are not going to vote for a debt limit increase no matter what. That means they’ll need at least about 30 Democrats, and probably a good deal more. If a deal is going to need close to half of House Democrats, then it almost certainly needs Nancy Pelosi.

The truly goofy thing about this whole mess is the outsized influence enjoyed by those 50 or so House Republicans that won’t be voting for any deal, no matter how much it might tilt towards conservative priorities. One would think that they’ve dealt themselves out. However, they — along with their slightly less rejectionist conservative collaborators — are the key restraint on John Boehner. As Jonathan Chait notes today, what their opposition does is make some of the deals that are mathematically possible into political poison for the Speaker. He isn’t going to endorse anything that won’t get the approval (in private at least — they may not vote that way) of a strong majority of the House Republican conference, because otherwise he risks a revolt.

For House Democrats, the best strategy (no surprise here) is unity. If they can maintain that, then they have quite a bit of leverage. If not, Boehner can start trying to pick off 25 or 30 or 35 Democrats, and perhaps he can make that work. My guess, however, is that ultimately nothing will pass unless it has genuine leadership support — and not just votes — from Democrats and Republicans in both chambers. Nancy Pelosi certainly knows that, and as the President himself said today, he’s very aware that he needs Democrats to get this done.

UPDATE: And Nancy Pelosi herself drew a firm line today against Social Security and Medicare cuts. “We do not support cuts in benefits for Social Security and Medicare,” she said at her presser today. “Any discussion of Medicare or Social Security should be on its own table.”