Ten of the 11 states with the biggest declines in their uninsured rates accepted the healthcare law's Medicaid expansion, which provides safety-net coverage for low-income residents, mainly adults with no children living at home. Topping the list were Arkansas and Kentucky, with double-digit decreases.
Montana, in the midst of an oil boom, was the exception among the top-performing states. Its uninsured rate dropped by 4.9 percentage points from 2013 to 2014, although that state has not expanded Medicaid and is letting the federal government run its online insurance market.
In addition to expanded Medicaid, Obama's law offers subsidized private coverage for people who don't have access to it on the job. The federal government is running the online insurance markets, or exchanges, in most states.
The Gallup report comes at a time of continuing uncertainty over the healthcare law. Next week, the Supreme Court will hear arguments in a case that challenges insurance subsidies for residents of states that have not set up insurance exchanges, defaulting instead to federal management. The federal HealthCare.gov currently serves 37 states.
The survey is considered authoritative because it combines the speed of media polls with the thoroughness of large government studies. Pollsters interview 500 people a day, 350 days a year. In 2014, that added up to nearly 177,000 adults aged 18 and older.
Comparing full-year results, Gallup found a drop of 3.5 percentage points in the share of Americans without health insurance from 2013 to 2014.
The five most populous states all saw declines. For California, it was a drop of 6.3 percentage points; Texas, 2.6 points; Florida, 3.8 points; New York, 2.5 points and Illinois, 4.5 points.
Texas remained the state with the highest uninsured rate, at 24.4%, while Massachusetts had the lowest, at 4.6%. Massachusetts had expanded coverage earliest, under former GOP Gov. Mitt Romney, whose approach foreshadowed some of the central elements of Obama's law.
Dan Witters, research director for the poll, said about 12.3 million fewer adults were uninsured in the last three months of 2014, when compared with the third quarter of 2013, when HealthCare.gov was launched.
The survey has a margin of sampling error of plus or minus 1 to 2 percentage points for most states. The ongoing survey plans to report in April on the law's impact in the first three months of this year.