The health care law's historic gains in coverage may be leveling off: The Obama administration announced Thursday it expects only a slight overall increase in enrollment next year.

With the 2016 sign-up season two weeks away, Health and Human Services Secretary Sylvia M. Burwell set a target of 10 million people enrolled and paying their premiums by the end of next year. That's about as many as are covered now through the law's online markets for subsidized private health insurance.

Burwell said it's getting harder to sign up the remaining uninsured. They tend to be young, managing very tight household budgets, and often unaware they can qualify for taxpayer-financed assistance with their premiums.

The administration's new target is well below an estimate from congressional budget analysts of about 20 million covered in 2016. The huge difference quickly raised questions about whether advances in health insurance coverage under President Barack Obama's law may sputter or stall, leaving millions still uninsured.

"If enrollment plateaus, we may see growing discussion of whether the law is fulfilling expectations in covering the uninsured, and whether the subsidies for low- and middle-income people are sufficient to make coverage truly affordable," said Larry Levitt, an expert on the law with the nonpartisan Kaiser Family Foundation.

Burwell called the new goal "strong and realistic." An aide said the congressional numbers are based in part on assumptions that haven't panned out, about employers dropping job-based plans for their workers, and about people with their own private coverage switching to HealthCare.gov.

Obama's law has reduced the share of uninsured Americans to about 9 percent through a combination of subsidized private insurance and a Medicaid expansion aimed at low-income adults. As documented by government studies and independent surveys, that's a historic accomplishment. But things may be changing.

Premiums are expected to go up next year by a bigger amount than this year. Surveys show that among the 10.5 million remaining uninsured who are eligible, many are young adults, a demographic that traditionally has not put a high priority on having health insurance. Many are unfamiliar with insurance terms like "premium," ''deductible," ''copays," and "networks." And money is a problem.

"We know that the remaining uninsured have a lot of concerns about whether they can afford coverage," said Burwell. "About half have less than $100 in savings."

Meanwhile, progress on the law's Medicaid expansion has largely come to a standstill. Although a majority of states have accepted expanded Medicaid, high-population southern states including Texas, Florida, Georgia and North Carolina continue to hold back because of entrenched political opposition to Obama's overhaul.

The administration said the new target of 10 million signed up for the law's private plans includes mainly customers renewing their coverage from this year, but also 3 million to 4 million people who are currently uninsured.

The insurance markets are now two years old, but they don't quite appear to have stabilized. Experts cite a combination of reasons:

— High turnover. Some people who sign up for a plan don't follow through and pay their first month's premiums. Among those who do obtain coverage, some later switch to an employer plan or qualify for Medicaid. Others drop out because they can't afford even their subsidized premiums. Turnover has always been a big part of the individual health insurance market.

— Costs. Private surveys back up the administration's findings that many uninsured often cannot spare even $100 a month for coverage, not to mention the out-of-pocket costs of medical care.

— Complexity. Getting and keeping coverage under Obama's law can be frustrating, especially when it comes to documenting eligibility for benefits. The administration said recently it terminated coverage for some 420,000 people who couldn't document that they were citizens or legal immigrants. And nearly 970,000 households had their subsidies "adjusted" because of problems documenting their incomes. Counselors who work with insurance customers say they are seeing many people whose subsidies were completely eliminated because of income reporting problems.

The new sign-up season for the law's private health plans starts Nov. 1 and runs through Jan. 31. People who don't have access to coverage on the job can pick a plan through HealthCare.gov and state-run insurance markets. About 8 in 10 will also be eligible for financial aid, which covers roughly 70 percent of premiums on average.