WASHINGTON — More than 10 million people have signed up for private health insurance this year under President Obama’s law, the administration said Tuesday. That puts the nation finally within reach of coverage for all, but it may not last.

The report from the Department of Health and Human Services comes as dozens of insurers are proposing double-digit premium hikes for next year, raising concerns about future affordability. And the Supreme Court is weighing the legality of subsidized premiums for millions of consumers in more than 30 states. A decision is due around the end of the month.

The 10.2 million sign-ups represent consumers who enrolled in a plan and followed through by paying their first month’s premiums. That number will fluctuate during the year as some people get jobs that offer coverage, and others decide to drop their insurance.

Although it exceeds a target of 9.1 million set last year by HHS Secretary Sylvia M. Burwell, it’s not much of a cushion. “Enrollment has been lower and slower than what most people projected,” said Caroline Pearson of the data analysis firm Avalere Health.

Still, the combination of subsidized private coverage sold through online insurance exchanges in every state, along with Medicaid expansion in most states, has resulted in historic coverage gains.

Nearly 9 out of 10 adults now have health insur.ance – about the same proportion who buckle their seatbelts.

Health insurance is now a federal mandate for most people, with employer plans remaining as the mainstay for workers and their families.

A major private survey, the Gallup-Healthways Well-Being Index, found 88 percent of U.S. adults have coverage.

The new health insurance numbers could be just an ephemeral high-water mark if the Supreme Court invalidates subsidies for people in states using HealthCare.gov, the federal government’s online exchange.

In the 34 states most directly affected, nearly 6.4 million people could lose subsidies worth more than $1.7 billion a month. Without financial assistance, it’s expected that most of those consumers would drop coverage. As healthy people exit the market, premiums would spike for the remaining customers buying individual health insurance policies.

The court case revolves around the literal meaning of a handful of words in the complex law.

Opponents say the law only allows subsidies in states that set up their own insurance exchanges. Only 13 states and Washington, D.C., are running their own markets this year. The administration says that, when read in context, the law allows subsidies in all 50 states regardless of whether the federal HealthCare.gov is in charge of sign-ups.

If the Supreme Court invalidates the subsidies, Republican-led states would bear the brunt of the coverage losses.