WASHINGTON — The nation’s uninsured rate dropped modestly this month as the major coverage expansion under President Barack Obama’s health care law got under way, according to a closely watched survey released today.

The Gallup-Healthways Well-Being Index found the uninsured rate for U.S. adults dropped by 1.2 percentage points in January, to 16.1 percent. 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 to 34. Members of that coveted, low-cost demographic have been ambivalent about signing up so far.