Near the end of the piece, Nyhan says, "Even after the insurance expansion is complete, it’s not clear that direct contact will correct the public's mistaken beliefs — remember the town hall participant who told a Republican congressman last summer to "keep your government hands off my Medicare?" This is a valid argument - but only to a point. Let's keep in mind that the subjects on which Nyhan has tested this effect are remote. The deficit may be a real thing, but to an individual it's an abstract calculation. Saddam's phantom weapons existed half a world away and we never saw them in the first place. So it can be easy to convince ourselves they were there all along, but were spirited away to Syria (the Hannity explanation.)
Health care, on the other hand, is something we actually experience. Nyhan correctly points out that many of the provisions of reform won't take effect for years, but once they do, people will have direct, personal experience with them. It will be awfully hard to tell people that, for instance, the insurance exchanges represent an assault on their freedom if they've actually visited their state's exchange and liked what they found. You can tell people that if a reform passes a government bureaucrat will be getting between them and their doctor, but it's much harder to tell them that a government bureaucrat is currently getting between them and their doctor if things between them and their doctor seem to be going just fine.
There are certainly opinions that won't be dented by the success of reform. But let's think again about that senior citizen telling government to keep its hands off his Medicare. He may be more distrustful of government than progressives would like. But one thing you can say about him is this: he loves his Medicare. Republicans know that, which is why they pretend they favored Medicare all along. If the same ends up being true of the system this reform puts in place, then that will be more than enough to celebrate.
This sort of scenario is plausible post-2014, but it will take time (most people don't interact with the health care system all that often). For instance, Pollster.com's Mark Blumenthal (who is a friend and allows me to cross-post to his site) discusses the lag in public support for the Medicare Part D prescription drug benefit:
[I]n the immediate aftermath of passage in early 2004, the Kaiser Family Foundation found that seniors were mostly negative about the new law (17% rated it favorably, 55% unfavorably). Their impressions did not begin to turn for more than two years when seniors finally started receiving their drug benefits.
While, as Brendan notes,"the most far-reaching changes" of the new law " won't take effect until 2014," there are narrower benefits that will begin this year, including a special insurance pool for those denied insurance due to pre-existing conditions, some insurance subsidies for small business, the closing of the Medicare Part D "donut hole" for seniors and a provision allowing young adults to remain on their parents' insurance policies until age 26.
In short, it took two years for public opinion to improve for a benefit that was essentially free -- though selecting plans was confusing for many, seniors received a major new benefit without accompanying tax increases, etc. The post-2014 reforms will include relatively more pain (mandates, tax increases, plan changes) and relatively less gain (especially for higher-income Americans), so I'd expect any subsequent increase in public support to take longer than Part D.
Also, it's worth remembering that the onset of the mandate will generate lots of ill will that will probably prime people to find reasons to dislike the system. Blumenthal notes that many Americans hear horror stories about health care via their social networks, but they're also likely to hear negative anecdotes about reform in the same way.
Ultimately, I do think the reforms will survive efforts to repeal them and become relatively popular, but it will probably take years.