President Obama calls them “substandard” insurance plans. But to many of the people who bought individual insurance policies that are now being canceled under the Affordable Care Act, their choice of insurance was a prudent decision that met their needs at a price that will be hard to beat under the ACA.

Jim Stadler is one of the “5 percenters”—the 5% of Americans with health insurance policies they purchased on their own—who got notified recently that their carrier was canceling coverage because it didn’t meet the tougher new minimum requirements of the ACA. Stadler, a freelance writer who lives outside of Charlotte, N.C., was laid off from a full-time job at an ad agency in 2009, at which point he became a freelancer and bought individual health coverage for him and his two kids.

Under Stadler’s expiring policy, his premiums are $411 a month, for coverage that always seemed adequate to him. “It’s not a substandard policy,” he says. “I thought it was a great deal.” The premium for the new policy offered by his insurer will be $843 a month, with coverage that’s more or less the same as far as he’s concerned. But new policies are required to include free preventive services such as mammograms and colonoscopies, and they can’t be canceled or priced higher for sicker people, which is why the cost of some policies is going up.

Since Stadler’s family’s income is too high to qualify for federal subsidies, he’s considering putting his kids on the policy his wife, a teacher, gets through her job. But that would be expensive, too. “The thing that gets me,” says Stadler, who voted for Obama in the 2012 presidential election, “is I thought Barack Obama was the only guy I could trust in Washington. He ended up lying to me because he said, if I like my insurance, I could keep it.”

The 5-percenter problem could end up being a much more serious albatross for Obamacare and its mostly Democratic supporters than the notorious web site snafus and other temporary snags, which can mostly be fixed. Obama did, in fact, say repeatedly, “If you like your health insurance, you can keep it.” But policies held by as many as 10 million Americans don’t meet the minimum requirements of the law and are now being canceled. Obama this week added a “vast majority” clause to his earlier claim: “For the vast majority of people who have health insurance that works, you can keep it,” he said in a recent speech on health-care reform.

Obama also continues to point out that many people whose insurance is being cancelled will get a better deal through one of the new exchanges, because of federal subsides offered to lower-income people to help them pay for coverage. The real losers, by contrast, are people like Stadler who won’t qualify for subsidies, and will no longer be able to buy “substandard” policies, either. Many such people will face higher costs for better coverage they wouldn’t choose to pay for on their own, which is exactly the type of Washington-knows-better policymaking that outrages Tea Partiers and many independents who think the government has become too invasive.