As House Republicans struggle to figure out whether their proposed response to the border crisis can pass the House, given opposition to action among conservatives, it’s increasingly likely they’ll need House Dems to get anything through the lower chamber.

So House Dems appear to be coalescing behind a response that essentially offers House Republicans two choices:

1) If you want to spend money to solve the short term problem, we’ll support that, but we won’t support any half-cocked or crazy legislative maneuvers that strip kids of legal rights and protections; or

2) If you really want to legislate here, let’s do comprehensive immigration reform. In other words, when it comes to legislating, it’s comprehensive immigration reform or nothing.

This morning, House Democrats met with Dem leaders and engaged in a spirited discussion over how to proceed. Republicans have proposed a response that includes $1.5 billion in funds, sending in the National Guard, and changes to the 2008 trafficking law that Dems fear could strip kids of needed protections. But some conservatives insist the measure include efforts to block Obama’s deferred-deportation programs, and others claim the GOP shouldn’t act at all. Why? As Steve King put it: “We’re putting our head in the noose and associating ourselves with the president’s problem.”

At today’s meeting some Dems argued that House GOP leaders have boxed themselves into an untenable position — if they lose too many conservatives, they can’t pass anything without Democrats — meaning they should renew the demand for a vote on comprehensive reform. Dems know there’s no chance Republicans would agree to any such vote. But they are hoping to use the occasion to remind people that there is a broader solution on the table Republicans won’t act on. Meanwhile, they will also argue that any short term fix should only focus on solving the crisis within existing law, rather than monkeying around with ill-thought-out “get tough” legal changes that are only designed to buy Republican votes.

“We’re ready to vote for the resources to address the large number of children who have come to the border,” Dem Rep. Lloyd Doggett of Texas told me. “But that’s a separate issue from whether the law should be altered. We take a firm line on that. It should not be used to hold the necessary funds for the border hostage.”

“There is growing unity among Democrats that now is the time to say, ‘Either fix the broken immigration system once and for all, and address all aspects of this problem, or if you are still unwilling to do that, despite this humanitarian crisis, at least provide funds to assure that we move these young people through the process,'” Doggett continued.

“We’re the ones holding the cards, not them,” Dem Rep. Joe Garcia of Florida added in an interview. “We have a solution. It’s called comprehensive immigration reform.” Garcia added that if Republicans are unwilling to seriously legislate, “this problem belongs to them.”

Nancy Pelosi put it this way today: “The most important thing that we can do to use this crisis as an opportunity is to pass comprehensive immigration reform.”

To be clear, Senate Democrats will have their own struggles with the issue; today Mary Landrieu balked at supporting the Dem plan to provide funding to address the crisis with no strings attached, suggesting other vulnerable Dems may follow.

But it’s increasingly sinking in that House Republicans, too, face serious political risk if they are unable to pass any response to the crisis. As Chad Pergram puts it: “Republicans worry they may ‘own’ the border calamity by moving a bill which can’t be resolved with the Senate or failing to pass a bill at all.”

From the perspective of Democrats, the really perverse thing here is that Republicans, after failing to vote on immigration reform for literally years, are now finally going to hold a real vote on something immigration-related, yet it is all about bolstering border security and could potentially hurt more children. And they want Democratic support to pass it. It’s not surprising, then, that Dems are increasingly inclined to say: No.