The U.S. uninsured rate dropped modestly this month as expanded coverage rolled out under President Barack Obama’s health care law, a major survey released Thursday showed.

The Gallup-Healthways Well-Being Index found that the uninsured rate for U.S. adults dropped by 1.2 percentage points in January, to 16.1 percent. That would translate to roughly 2 million to 3 million people gaining coverage.

The closely-watched poll combines the scope and depth found in government surveys with the timeliness of media sampling. Pollsters interview 500 people a day, 350 days a year. The survey can be an early indicator of broad shifts in society. The health care results were based on more than 9,000 interviews, about nine times as many as in a standard national poll.

“The uninsured rate had been expected to come down as the Affordable Care Act was implemented,” said Frank Newport, Gallup’s editor-in-chief. “That would be the most reasonable hypothesis.”

The biggest change was for unemployed people, a drop of 6.7 percentage points. That was followed by a 2.6 percentage-point decline for nonwhites. Traditionally both groups are far more likely to be uninsured than the population as a whole.

The survey found no appreciable change among young adults ages 18-34. Members of that coveted, low-cost demographic have been ambivalent about signing up so far — though their insurance purchases are considered key to defraying the cost of other provisions of the law, such as its ban on denying insurance to those with pre-existing condition.

Women saw a decline of 1.9 percentage points, about three times greater than the 0.6 percentage-point drop for men. Uninsured rates also fell all along the income ladder, with those making $36,000-$89,999 seeing the greatest drop, 1.8 percentage points.

Medicaid sign-ups are also rising. That’s partly because of a program expansion accepted by half the states and partly as a consequence of previously eligible but unenrolled people complying with the law’s individual coverage mandate.

The White House called the poll good news. “It shows that the law is working,” said David Simas, a senior adviser.

Nonetheless, Newport said it could take a calendar quarter — three months — to discern a full trend. Other factors could also be behind the shift, including an improving economy.

“It’s a drop, but not extraordinary,” said Newport. “The glass is half full for proponents of the Affordable Care Act because things are moving in the right direction. But the glass is half empty because things haven’t moved much.”

The office of Senate Republican leader Mitch McConnell pointed out that the adult uninsured rate is about the same now as when Obama took office in 2009. It has gone as high as 18.6 percent during his term.

Gallup’s numbers are not comparable to various figures cited by the Obama administration, estimates that have ranged to more than 9 million people benefiting.

For starters, the administration’s numbers include children as well as adults. They combine people buying coverage in the new insurance exchanges, Medicaid enrollees, and young adults who can stay on a parent’s plan until they turn 26.

But the administration doesn’t break out figures for those who were previously uninsured. Some of those signing up for new plans may have already had insurance; they either had to switch coverage because of the law or they found a better deal.

The law is projected to eventually drive the uninsured rate down to single digits among legal U.S. residents. But its troubled rollout has raised questions about whether it can achieve that goal.