WASHINGTON — Insurance cancellations are fueling a political backlash against President Obama and Democrats supporting his health care overhaul.

The president apologized Thursday for the turmoil some consumers are going through, but there may yet be a silver lining as far as the law itself.

It’s Economics 101, a little-noticed consequence of a controversial policy decision. And there are winners and losers.

Millions of people who currently buy their own health insurance coverage are losing it next year because their plans don’t meet requirements of the health care law. But experts say the resulting shift of those people into the new health insurance markets under Obama’s law would bring in customers already known to insurers, reducing the overall financial risks for each state’s insurance pool.

That’s painful for those who end up paying higher premiums for upgraded policies. But it could save money for the taxpayers who are subsidizing the new coverage.

“Already-insured people who do roll over will improve the risk pool, not hurt it,” said David Axene, a California-based actuarial consultant for health plans, hospitals, government programs and employers.

Compared to the uninsured, people with coverage are less likely to have a pent-up need for medical services, he explained. They may have already had that knee replacement instead of hobbling around on a cane. They’re also more likely to have seen a doctor regularly.

“The current individual market enrollees are definitely a good addition to the risk pool,” concurred Larry Levitt, an insurance expert with the nonpartisan Kaiser Family Foundation.

At some point, all these customers had to pass extensive medical screening that insurers traditionally use to screen out people with health problems. Such filtering will no longer be allowed starting next year, and a sizable share of the uninsured people expected to gain coverage under Obama’s law have health problems that have kept them from getting coverage. They’ll be the costly cases.

Obama had sold his health care overhaul as a win all around. Uninsured Americans would get coverage and people with insurance could keep their plans if they liked them, he said. In hindsight, the president might have wanted to say that you could keep your plan as long as your insurer or your employer did not change it beyond certain limits prescribed by the government.

That test proved too hard for many plans purchased directly by individuals, leading to a wave of cancellations affecting at least 3.5 million people, based on an AP survey in which about half the states reported data.

“I am sorry that they … are finding themselves in this situation, based on assurances they got from me,” Obama said in an NBC interview, adding that the administration will do “everything we can” to help.

The new plans under Obama’s law generally guarantee a broader set of basic benefits and provide stronger financial protection in cases of catastrophic illness.

“There is change coming to the individual marketplace with consumer protections that many people have never enjoyed or experienced,” Health and Human Services Secretary Kathleen Sebelius told senators this week.

But better coverage also costs more.

“The loser is the consumer who is paying higher premiums to subsidize Obamacare, and who was paying lower premiums because they were in another plan before,” said Bob Laszewski, a health care industry consultant critical of the law.

A new study by the Kaiser Family Foundation found that people who already have individual coverage are less likely to qualify for the tax credits that will make coverage more affordable through the health law’s insurance markets.