WASHINGTON (AP) — Not only do more Americans have health insurance, but the number struggling with medical costs has dropped since President Barack Obama's health care law expanded coverage, according to a study released Thursday.

The Commonwealth Fund's biennial health insurance survey found that the share of U.S. adults who did not get needed care because of cost dropped from 43 percent in 2012 to 36 percent last year, as the health care law's main coverage expansion went into full swing.

The proportion of people who got treatment but had problems paying their bills also dropped, from 41 percent in 2012 to 35 percent last year.

It was the first time that either measure of financial distress declined since the survey began asking the questions, in 2003 and 2005, respectively.

"Expanded insurance coverage is helping people get the care they need by reducing financial barriers to care," the study said.

The health care law offers subsidized private insurance to people who don't have coverage on the job, combined with expanded Medicaid in states that agree to broaden eligibility for that safety-net program.

Soon after the coverage expansion launched last year, a large ongoing survey by Gallup started documenting a sustained drop in the number of uninsured people. The Commonwealth Fund survey fills out that picture by adding details about the affordability of care.

The New York-based Commonwealth Fund is a private foundation dedicated to expanding coverage and improving the quality and cost-effectiveness of the health care system. While those goals generally align with Obama's health care law, the group is nonpartisan.

The findings come at a crucial juncture for Obama's law, as the Supreme Court prepares to hear another challenge from opponents committed to rolling it back. Republicans newly in charge of Congress are also planning more repeal votes.

Plaintiffs in the court case argue that the law as written only allows the federal government to subsidize coverage in states that have set up their own insurance markets. Supporters of the law say that while its wording may be confusing, Congress intended for subsidies to be available across the country, regardless of state actions.

Since Washington is currently running the insurance markets in 37 states, a ruling favoring of the plaintiffs would unravel coverage gains in many states.

Among the survey's other highlights:

—The improvements in affordability are tempered. Many insured people still have problems paying medical bills, partly due to skimpy coverage that shifts costs to patients. That puts even many low-income workers with health insurance in a predicament. Thirty-three percent of insured adults with incomes under 200 percent of the federal poverty level ($47,100 for a family of four) said they did not get needed care in the past year because of costs.

—While nationally the share of Americans without health insurance declined from 20 percent in 2010 to 16 percent by the second half of 2014, a divide has opened between states that agreed to expand Medicaid and states choosing not to. Thirty-five percent of adults below the poverty line remained uninsured in states that did not expand eligibility, compared with 19 percent in states that did.

—Hispanics continued to lag other ethnic groups in coverage, despite the health care law. In 2014, 34 percent of Latinos were still uninsured, compared to 18 percent of African Americans and 10 percent of whites.

The Commonwealth Fund survey was conducted by Princeton Survey Research Associates International from July 22 to Dec. 14, 2014. The report's analysis was based on interviews with 4,251 adults age 19-64. It has a margin of sampling error of plus or minus 2 percentage points.