WASHINGTON » Sign-ups under President Barack Obama’s health care law grew slowly but steadily over the New Year’s holiday, as the share of Americans still lacking coverage hit its lowest level in years.

The Obama administration reported Wednesday that nearly 103,000 people signed up last week in the 37 states where the federal government is running online health insurance markets, bringing total enrollment to 6.6 million in those states. The remaining states, which include Hawaii, are running their own exchanges. (The Hawaii Health Connector had enrolled 15,552 as of Monday, up from fewer than 500 a year ago.)

Meanwhile, a new Gallup survey found that 12.9 percent of the adult population remained without coverage in the last three months of 2014, the lowest share since the pollster began daily tracking of the uninsured in 2008, before Obama took office.

The Gallup-Healthways Well-Being Index found that the uninsured rate dropped 4.2 percentage points over the past year as the health law’s major coverage expansion went into effect. Other analysts have estimated that those gains translate to at least 10 million uninsured people getting coverage. A year ago 17.1 percent of adults were uninsured.

"The Affordable Care Act has accomplished one of its goals: increasing the percentage of Americans who have health insurance coverage," Gallup concluded.

Obama’s law offers subsidized private insurance to people who don’t have coverage on the job, along with expanded Medicaid coverage for low-income people. Insurers can no longer turn down people with health problems. Virtually all individuals are required to have coverage or risk a fine.

Some of the insurance gains are no doubt due to an improving economy, but Gary Claxton of the nonpartisan Kaiser Family Foundation said, "It’s hard to deny that the sharp reduction in the uninsured in 2014 was (caused by) the law." Claxton helps direct the foundation’s widely cited annual survey of employer plans.

Wednesday’s report from the Health and Human Services Department comes as the health law’s second open enrollment season has passed the halfway mark. So far, there hasn’t been the technology meltdown that marred the first sign-up season. Insurers also say automatic renewal for millions of last year’s customers has gone fairly smoothly.

But Obamacare remains controversial. Republicans who took charge of Congress this week remain committed to repealing the law.

And the Supreme Court has agreed to hear a case that challenges the legality of subsidies in states where Washington is running the insurance markets. More than 8 in 10 customers are getting financial assistance, which covers about three-fourths of their premiums on average.

If the Supreme Court agrees with the plaintiffs in the case, those subsidies would end and much of the insurance coverage gains could evaporate.

The Obama administration says it is confident it will prevail in the court case, and is urging consumers to keep signing up. Feb. 15 is the last day of open enrollment. The administration wants 9.1 million customers signed up and paying premiums in 2015.

Gallup’s survey has a margin of error of plus or minus 1 percentage point for results based on the total sample.