WASHINGTON — While states are having varying success getting people to sign up, January marked the first time since new health insurance markets opened last fall that a national monthly enrollment target was met.

The administration said Wednesday about 1 million people signed up for private insurance under President Barack Obama’s health care law in January, extending a turnaround from early days when a dysfunctional website frustrated consumers.

An Associated Press analysis found that most states are still lagging when it comes to sign-ups under the health care law, and their success in getting those sign-ups could help determine if the White House reaches its unofficial goal of having 7 million signed up by the end of March. Nearly 3.3 million people signed up from Oct. 1 through Feb. 1.

About a dozen states are high achievers in getting sign-ups.

Connecticut is the nation’s top performer, signing up more than twice the number of residents it had been projected to enroll by the end of January. Massachusetts, which pioneered the approach Obama took in his law, is at the bottom of the list, having met only 5 percent of its target.

Six Republican-led states — Florida, Idaho, Maine, Michigan, North Carolina and Wisconsin — are on pace or better. Residents are signing up despite strong political opposition to the health care law in some of those states.