Today’s CNN poll (PDF) on the Affordable Care Act seems like a blow to supporters of the law. When asked if they “generally favor or generally oppose” the president’s health care overhaul, only 35 percent say they “favor.” The large majority—65 percent—say they “oppose.”

For Republicans who have staked their entire message on opposition to Obamacare, this looks like vindication. Not only was the rollout a disaster, but now, the public has turned decisively against the effort. Why would they stop the attacks and calls for repeal if Americans are united in disdain for the law?

The problem for Republicans—and the good news for supporters—is that the results are a little more complicated than they look. In addition to the binary question about support or opposition, CNN also asked respondents to explain their position on the law. Do they oppose the legislation because it’s too liberal, or do they oppose it because it’s not liberal enough.

The answer, for 15 percent of Americans, is that they oppose the Affordable Care Act because it’s not liberal enough in its approach toward health care reform. Indeed, when you look at the full results, you see an electorate that either supports Obamacare or wants a more liberal alternative. There’s still an open question as to what those 15 percent want, but—if they support more liberal policies—then it’s fair to say they don’t want to dismantle the law. What Republicans want—a majority that opposes Obamacare and wants its repeal—just doesn’t exist.

Of course, no one (or at least, no one with credibility) believes that Congress will repeal the Affordable Care Act. The barriers are just too high, and by the time its even possible—2017, if Republicans win the Senate in 2014, abolish the filibuster, and win the presidency in 2016—millions of Americans will have already received benefits from the law, to say nothing of the hospitals and insurance companies that will oppose an abrupt return to the status quo ante.

But none of this reality has stopped Republicans from placing their opposition at the center of their approach to next year’s elections, which is why this poll is relevant. If the public isn’t keen on destroying the Affordable Care Act, then there’s a limit to how much the GOP can gain from running this playbook.

Now, a lot depends on the success of the law and the geography of public opinion. If pro-repeal votes are concentrated in red states where Democrats are playing defense, then this broader dynamic doesn’t matter as much. But, if voters are ambivalent on the law—and open to strong arguments and good results—then next year might end with a little Republican disappointment.