I’m not sure it’s fully appreciated just how dangerous a political game House Republicans are playing on immigration right now. Far right Republicans in the House are not just at risk of taking the blame for killing immigration reform. It’s potentially worse than that: They are at risk of taking the blame for killing the immigration overhaul over health care reform, something that is broadly popular among Latinos.

Consider what is happening with the negotiations among the House “Gang of Eight” over their own immigration plan right now. Here’s what we know: GOP Rep. Raul Labrador, a key voice in the House on immigration, walked away from the House Gang of Eight talks last night because of differences over health care. In the statement Labrador released last night, his office said he could no longer support the emerging House compromise unless it required “that illegal immigrants would be responsible for their own health care costs, principally through requiring them to purchase health insurance.”

A source close to the talks tells me that Labrador wanted undocumented immigrants who don’t cover their own health care costs to face deportation. What this would appear to mean, in effect, is that any undocumented immigrant might face a choice between not seeking, say, emergency room care (which would ultimately be covered by government) and potential deportation. (A Labrador spokesman didn’t immediately comment.)

What that source tells me isn’t all that far off of a recent Los Angeles Times report, which said Republicans were balking at the House Gang of Eight talks because they wanted those on the pathway to citizenship who don’t purchase their own health coverage to face deportation. Dems have denounced this as too harsh, since many of them might be unable to afford their own coverage.

To be fair, Republicans dodged a bullet here in the last 24 hours, because the House “Gang of Eight” agreed to proceed with their talks without Labrador. And the word right now is that the House compromise language is beginning to resemble that in the Senate compromise, which prohibits those on the path to citizenship from getting subsidies to participate in Obamacare exchanges but won’t punish those who seek emergency care with deportation.

Still, the concerns Labrador apparently walked out over illustrate just how far to the right some in the GOP caucus are on immigration. Indeed, it comes after House Republicans voted today in overwhelming numbers to approve an amendment — put forward by diehard anti-immigration reform dead-ender Steve King — that would take away the funding that gives the Obama administration flexibility to stop the deportation of the DREAMers, as opposed to those convicted of crimes.

As the House Hispanic Caucus put it: “House Republicans just voted to treat DREAMers and undocumented spouses of servicemembers in the same way as violent criminals.”

All of this illustrates the depth of hostility among House Republicans towards immigration reform. And the health care angle adds another dimension, one that underscores that Republicans are seriously at risk of setting back their efforts to repair relations with Latinos even further. After all, Mitt Romney recently diagnosed his own 2012 loss by flatly admitting that his campaign had underestimated the appeal Obamacare has for minorities. Now Republicans are at risk not just of killing immigration reform, but of killing it in part because of their hostility towards Obamacare. As Labrador himself put it yesterday:

“What might be the story at the end of this year, at the end of this session, is that Obamacare killed immigration reform.”

That doesn’t seem like a particularly good “story” for Republicans, does it?