WASHINGTON — President Obama’s legacy health care law has reduced the number of Americans going without health insurance to historically low levels, but continued progress threatens to stall this year, according to a new government report.

The study released Thursday by the Centers for Disease Control and Prevention suggests the law may be reaching a limit to its effectiveness in a nation politically divided over the government’s role in guaranteeing coverage.

The CDC said the number of uninsured people dipped by only 200,000 between 2015 and the first six months of this year, which it called “a nonsignificant difference.” The findings come from the National Health Interview Survey, which has queried more than 48,000 people so far this year.

Since the health care law’s big coverage expansion in 2014, millions have gained coverage each year. Now the pattern appears to be changing.

Experts say Obama’s overhaul deserves most of the credit for 20 million Americans gaining coverage since 2014. But progress has been less and less each year, and now it’s slowed to a crawl.

“It has got to be close to tapped out,” said Dan Witters, director of a major private survey that also follows insurance trends, the Gallup-Healthways Well-Being Index.

The CDC study found that during 2015, an estimated 28.6 million U.S. residents were uninsured. The corresponding number through the first six months of 2016 was 28.4 million.

The sobering numbers come as the administration seeks to whip up enthusiasm for the 2017 sign-up season, which started this week and runs through Jan. 31.