A sizable number of House Republicans can be expected to vote against the eventual debt ceiling compromise on ideological grounds, something you’d think would give House Dems a bit of leverage in these negotiations. After all, House leaders will presumably need a sizable bloc of Democrats in order to pass the compromise through the House. So this should give them a say over the outcome of the talks. Right?

Well, no, not necessarily. All signs right now are that the White House is proceeding as if House Dem support can simply be taken for granted. After all, House Dems have made it clear that they don’t support any cuts to Social Security or Medicare, and yet that’s exactly where the talks appear to be headed.

This morning, in the wake of news that the White House is offering major entitlements cuts in exchange for $1 trillion in revenues from Republicans, the Congressional Progressive Caucus again laid down their marker, shooting off a letter to the White House saying they can’t support such a bargain. It reads:

First, any cuts to Social Security, Medicare and Medicaid should be taken off the table. The individuals depending on these three programs deserve well-conceived improvements, not deep, ideologically driven cuts with harmful consequences. These cuts would hurt households and damage the country’s economic recovery as well.

Second, revenue increases must be a meaningful part of any agreement. Tax breaks benefiting the very richest Americans should be eliminated as part of this deal. Republican insistence on protecting these tax breaks will force middle-class families to shoulder the burden of even deeper budget cuts, and this is unacceptable.

Do House Dems have any prayer of exerting leverage over the talks in service of realizing even a smidgen of what they want?

Dem Rep. Peter Welch is urging fellow liberals to vote No on the debt ceiling compromise if it’s a bad deal, on the idea that it’s the only way House Dems can break a dynamic which continues to leave them with little influence.

Ultimately, though, the question of whether House Dems can exert any leverage over the talks lies with Nancy Pelosi and Steny Hoyer. As E.J. Dionne notes today, if a sizable bloc of liberals can be counted on to vote No, that could actually strengthen the position of Pelosi and Hoyer, since GOP leaders will be relying on them and a sizable number of middle-of-the-road House Dems to vote Yes.

Pelosi, of course, has been urging Dems not cave on cuts to Medicare benefits. If history is any guide, of course, many House Dems will ultimately support the eventual deal once the President asks them to for the good of the party, his presidency, and the country. But if Pelosi holds firm — and persuades Obama and John Boehner that enough House Dems agree with her to make passage difficult — it’s not inconceivable that she can help bring about a deal that isn’t quite as terrible as the one we’re all expecting.