Way back in December 2012, House Speaker John Boehner helped set the tone for how Republicans would handle unwelcome policy developments in the second half of the Obama epoch.

If you’ll recall, the country was facing down the “fiscal cliff,” a mix of spending cuts and tax increases scheduled to automatically go into effect unless Congress and the White House moved quickly to legislate a way out of it. The Bush tax cuts were going to expire, and President Obama wanted to maintain the cuts for everyone making less than $250,000, but Republicans were opposed to tax increases of any kind.

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As the White House and Senate negotiated, Boehner threw the whole process into chaos by introducing his own plan that would raise taxes on millionaires only. Obama threatened to veto it and Harry Reid called it a non-starter, but their objections ended up being moot as Boehner couldn’t get enough support among House Republicans, who wouldn’t agree to any sort of tax increase, even for just millionaires. The plan failed, Boehner recessed the House, and everyone else stood blinking in disbelief trying to figure out what to do next. When the tax compromise did finally pass, House Republicans voted against it by a 2-1 margin.

What happened in that instance was that Republicans, faced with an inevitable policy outcome – the raising of tax rates – stuck firm to an absolutist position, knowing full well that it stood zero chance of success. They set a political trap for themselves and, without a moment’s hesitation, walked right into it. With the political landscape surrounding Obamacare undergoing considerable shifts of late, the Republicans look ready to repeat the process and risk sabotaging their own interests.

In the last week, Republicans have left no uncertainty that the only amount of Obamacare they will accept is zero. Ted Cruz redeployed one of his well-worn tropes in a speech at this past weekend’s New Hampshire Freedom Summit, telling the gathered activists that “we are going to repeal every single word of Obamacare.” Rep. Tom Cotton, R-Ark., who is running to unseat Sen. Mark Pryor, D-Ark., told reporters on Sunday that he would “repeal Obamacare and replace it entirely.” House Republicans passed the latest iteration of the Ryan budget, which prescribes repealing all of Obamacare and replacing it with some as-yet-unspecified free-market healthcare sorcery. Earlier in the month, Paul Ryan himself offered a stark assessment of the post-Obamacare future, saying that they’ll gut everything and won’t bring back the parts of the law people actually like.

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But here’s the thing: Obamacare isn’t going to be wiped clean from the earth. Too many people have been insured through Medicaid, too many people are covered through their parents’ plans, and too many people have purchased plans through the exchanges. To undo all that with a stroke of a pen would be catastrophic.

At a certain level, Republicans know this and are coming to grips with it. But they have too much invested politically in the repeal message to switch it up. That’s how you explain last week’s bizarre maneuvering by the House Republican leadership, in which they rushed through a voice vote on legislation to expand small-business coverage options under Obamacare and tried to keep it hush-hush. They think the full repeal message is a political winner and don’t want to be seen palling around with Obamacare.

But the scorched-earth approach to the Affordable Care Act is growing more and more incompatible with public sentiment. Gallup released its latest polling on the ACA last week, and while the top-line numbers show continued public dissatisfaction with the law, the internals tell a more nuanced story. Asked how they think the law will affect their healthcare situation in the long run, 32 percent said it will make it worse – an 8-point drop from Gallup’s previous survey. At the same time, 42 percent said it would make no difference at all, a 6-point spike.

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What’s likely happening is that as the Affordable Care Act eases itself into implementation, people are starting to see their firsthand interactions with Obamacare (or lack thereof) conflict with the political caricatures that have thus far formed the basis for understanding the law. Gallup’s finding dovetails with the Kaiser Family Foundation’s poll from late March, which found that Americans are actually getting fed up with the Obamacare debate and want to move on. “Just over half the public (53 percent) say they’re tired of hearing about the debate over the ACA and want the country to focus more on other issues.”

So why are Republicans sticking with full repeal when they know it’s not likely to happen and everyone else is sick of hearing about it? This adherence to the absolutist position is itself the inevitable consequence of a party that retreats further within itself in the search for electoral success. Dig into that Kaiser poll again and you’ll see that while Obamacare repeal is supported by only 29 percent of the public, a full 58 percent of self-identified Republicans want the law either scrapped and replaced or just plain scrapped. Repeal-minded Republicans aren’t building a coalition; they’re riling up the base and trusting that the Democrats will stay home in November.

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They are also, to a certain extent, boxed in by their own allies. The Koch brothers and other outside spending groups are spending millions to return control of the Senate to the Republicans. Those groups really, really hate Obamacare and have no tolerance for anything short of full destruction of the law. If Republican leaders look to be wavering in their commitment to repeal, they risk driving a wedge between themselves and some of their most potent backers.

Obviously the politics of healthcare reform in 2014 aren’t nearly as toxic for the GOP as the tax debate was back in 2012. But by hewing to the hard-line repeal position, Republicans have nonetheless put themselves in an awkward position as they play to an activist base that won’t tolerate a law that isn’t going anywhere.