The question of whether the GOP can repair its relationship with Latinos is often said to turn on whether Republicans will embrace immigration reform. But it’s also worth noting that Republicans may be making things worse with that demographic with their extreme tactics to defund or delay Obamacare.

In other words, current House GOP extremism could conceivably mean Republicans are setting themselves up for a kind of double whammy among Latino voters, as the image hardens among them of a GOP that is implacably opposed to addressing not just one, but two, problems of serious concern to them.

Polls show Latinos are more favorably disposed towards Obamacare than the public at large. A recent Pew poll found that 61 percent of Hispanics approve of the law. A Kaiser poll from August found 52 percent view the law favorably.

Mitt Romney, who lost among Latinos by enormous margins in 2012, partly costing him the election, has explicitly cited Obamacare as a reason he lost so badly among minorities, noting that his campaign “underestimated” the law’s “attractiveness” to them, particularly among “lower incomes.” Romney, of course, may have meant that there is no way he could have won among the “takers,” i.e., those voting for Obama in hopes of a government handout.

But Romney’s formulation does get at a core truth, which is that Latinos have a favorable view of activist government that could also put them at odds with Republicans over their efforts to repeal the health law and the expansion of the safety net it could represent. A Pew poll in 2012 found that 75 percent of Latinos favor a “bigger government with more services.”

“Latinos have an expectation that government will fulfill certain basic services and health care is one of them,” Fernando Espuelas, who hosts a popular call-in radio show on Univision, tells me.

Espuelas says the topic of health care and the Affordable Care Act in particular is a regular one on his show. While Espuelas says the administration could do a better job of explaining Obamcare’s benefits to Latinos, he also notes that administration officials have appeared regularly on his show to talk to Latino listeners about the law — a good move on the administration’s part — and that the GOP push to repeal the law could conspire with immigration to work against Republicans later.

“This can be used against Republican candidates or incumbents who have voted against Obamacare over and over again, especially in certain districts with more and more Hispanics,” Espuelas says, adding that Hispanics see health care and Obamacare in the context of economic issues: “The two things are very interconnected.”

As longtime Democratic strategist Simon Rosenberg puts it:

For those Republicans worried about getting their party right with the new American electorate, I would be more than a bit concerned about the current attack on the Affordable Care Act.  No group will benefit more from the ACA than Hispanic Americans.  Estimates are that as many as 10 million Hispanics could gain health insurance in the coming years due to the new American health care system.

The Republican narrative to them this week, just days before the ACA kicks in?  We are so committed to denying you health insurance that we are not just opposed to the ACA, but are willing to shut the government down, default on our obligations, and throw the US and global economy into chaos to make sure you don’t get it.

On both immigration and health care, the current GOP strategy is being shaped largely by the obsessions of its most radical lawmakers and voices. The GOP may be placing the Tea Party wing before the need to improve its appeal among a crucial, fast-growing demographic on not one, but two, major issues.