With Sen. Marco Rubio (R-Fla.) threatening to bail on his own bill, support for immigration reform in the Senate suddenly looks a lot shakier. And in the House, it may already be dead.

The issue that might have killed it: The debate over whether immigrants should get access to government-sponsored health care during their 15-year path to citizenship, sources told ABC News. Democrats argue that immigrants who pay taxes should be eligible for health benefits. Some Republicans disagree.

Rep. Raul Labrador (R-Idaho), a member of the House's Group of Eight, has already stepped away from the negotiating table over the issue.

"If they are going to have the benefit of living in the United States — which is a privilege, not a right — they should provide their own health insurance," Labrador told Roll Call.

Why the fixation on health care? Because Republicans are obsessed with defeating ObamaCare, argues New York's Jonathan Chait:

The trouble here... is that House Republicans' hatred of ObamaCare is at such deranged levels that it is leeching into even largely unrelated problems. The House Democrats are arguing that the newly legalized immigrants will pay taxes, so they should have access to government benefits. And Republicans don't seem to be suggesting they must be excluded from Social Security or denied access to national parks.

But ObamaCare is in a different category in their minds — a law so illegitimate and evil that nothing can be allowed to touch it at all.[New York]

It was only months ago, still feeling the sting of the brutal election results, that Republicans seemed willing to compromise in order to pass some kind of immigration reform. The Republican National Committee released a 98-page "autopsy" warning the GOP to cater to Latino voters or else watch its support die away as the demographics of the country continue to change. Rubio, the GOP's rising conservative star, even decided to become the public face of the Senate's bipartisan immigration bill.

But now, in both the Senate and the House, the political tone has changed. The GOP no longer feels the need to compromise, MSNBC's Zachary Roth says, because the IRS and Benghazi scandals have given them confidence:

The Beltway media has bought into [the scandals] just enough to create, at least temporarily, a storyline about an administration dogged by political controversy. And that's led Washington Republicans and their conservative allies to believe that they can ride that storyline back to power — just as they tried to do in the late 1990s with the Clinton impeachment....

[Republicans] see a potential way to win back the Senate next year and the White House in 2016 without having to alienate their core supporters by backing immigration reform. So their motivation for getting behind the project has gone out the window. [MSNBC]

What does that mean for immigration reform? Perhaps that no comprehensive bill will be passed in the House. Instead, congressmen may just try to pass piecemeal legislation.

"The whole reason the House has been making the Senate go first is so that compromise-averse House Republicans can avoid reaching agreement on things, even if they want them to pass," writes The Washington Post's Jonathan Bernstein. "Republican immigration voters may not like immigrants — but what they really hate is for Republican politicians to agree with Democrats on anything."