If you like daft ironies, here’s one to chew on today. It was three years ago this week that President Obama signed the greatest piece of social-justice legislation this country has seen in decades. Since its enactment on March 23, 2010, the Affordable Care Act has curbed the health insurance industry’s worst abuses, placed basic coverage within reach for a generation of young adults, and made birth control more accessible to reproductive-age women. Within months, the act will extend health coverage to millions of uninsured Americans by expanding Medicaid and spawning a new market for individual plans. And how are Americans marking the occasion? We’re achieving near-record levels of hostility toward the whole enterprise.

In its latest tracking poll, released earlier this week, the Kaiser Family Foundation found that just 37% of Americans now approve of Obamacare, while 40% oppose it. While small minorities (15% to 21%) expect to benefit from health care reform, nearly three in 10 believe it will leave them worse off. The partisan divide is still sharp (58% of Democrats in favor, 68% of Republicans opposed). But opponents have outnumbered supporters in 25 of Kaiser’s 34 polls since 2010, and both parties now stand at their second-lowest approval levels yet. Independents are disenchanted too, with 45% opposing health care reform and 31% favoring it. For all the resistance, you’d think the president wanted to ban oversize sodas.

But here’s the catch. People may dislike “the health reform law” when asked about it that way, but their negative views are rooted largely in ignorance. Strong majorities favor most of the law’s key provisions. Two-thirds favor the so-called guaranteed issue, which bars discrimination against people with pre-existing conditions. More than 70% support expanding Medicaid to cover people living below 138% of the poverty level. Some 76% like the rule that allows kids to stay on their parents’ plans through age 25, and even higher proportions favor health insurance exchanges, better drug coverage for Medicare participants, and tax credits to help small businesses sponsor health plans for their employees (chart). All told, the public favors 10 of Obamacare’s 11 key provisions, and Republicans favor seven of the 11. The only feature lacking majority support is the so-called individual mandate, which requires everyone to get some kind of coverage (since everyone will eventually need care). That rule―a Republican idea that Obama borrowed in an early attempt at bipartisanship―was upheld by the Supreme Court last summer.

What’s going on here? How can the public oppose the health care law while favoring almost everything about it? The short answer is ignorance. The new poll finds that our knowledge of the Affordable Care Act has atrophied selectively over the past three years. We’re slightly more aware of the individual mandate than we were in 2010, but less knowledgeable about the act’s more popular provisions. In April 2010, 64% of respondents knew the law would keep insurers from turning away people with pre-existing conditions. Today only 53% understand that. Likewise, 75% of Americans once knew that Obamacare included tax breaks to help people with moderate incomes pay for coverage. Today the figure is 62%. No wonder so many people expect to suffer.

These skewed perceptions are no accident. Opponents have spent four years seeding baseless fears about health care reform. The attacks dominated news stories in 2009 and 2010, when interest was high and the coverage emphasized politics and strategy over the substance of the act. The news coverage has slowed since then, and journalists have worked diligently to correct misrepresentations, but the charges have stuck. “Reporters have fact-checked and challenged the claims about death panels and benefit cuts,” says Drew Altman, the Kaiser Foundation’s president and CEO. “But the charges still get reported and repeated, and they shape people’s perceptions.”

Insurance exchanges will crop up all over the country early next year, and at least 26 states will expand their Medicaid programs, just as seven in 10 Americans think they should. As more Americans experience Obamacare first-hand, the resistance may soften, but don’t count on it. As Altman observes, many newly insured people will get their coverage through state programs with friendly names like “BadgerCare” or “Healthy Kids,” and some of them will go right on fearing the law that made it possible. Meanwhile, millions of us will keep snatching up best-sellers like Beating ObamaCare (which promises to help you “protect your money” by finding out “who gets a free ride”) and the ObamaCare Survival Guide (a “must read for anyone who is worried,” according to health expert Donald Trump).

But I’m going to raise a glass Saturday to what Dick Morris calls “the shocking impact of this radical plan.” It will save money and lives in the long run, and it’s already making mine easier. As someone who recently beat stage-4 (metastatic) colon cancer, I might now be uninsurable if the Affordable Care Act didn’t protect me. Under Obama’s radical plan, I’m still a full citizen with a crisp new insurance card.