WASHINGTON — Thousands of people signing up for health insurance this weekend may not realize it, but their coverage under President Barack Obama’s law could be short-lived.

The 2015 enrollment season, which ends Sunday, has avoided last year’s website meltdown so far. But a Supreme Court case could result in millions of consumers losing financial assistance for their premiums later in the year.

The Affordable Care Act still sits on shifting political sands.

“This would be devastating,” said Nita Carter, who oversees statewide enrollment efforts for UHCAN Ohio, a health care advocacy group. “Without the subsidy, health insurance will be unaffordable for many. If it is unaffordable, then it is not accessible.”

The Supreme Court case, called King v. Burwell, is the talk of Washington policy experts. But a recent Kaiser Family Foundation survey found that more than half of Americans have heard “nothing at all” about it and another 30 percent “only a little.”

The health care law offers subsidized private coverage to people who don’t have access to it on the job.

However, “ObamaCare” opponents who brought the lawsuit argue the law’s literal wording allows the federal government to pay those subsidies only in states that have set up their own insurance markets, or exchanges. Most haven’t.

The administration and Democratic lawmakers who wrote the law say Congress’ clear intent was to provide subsidies to people in every state.

If the plaintiffs succeed, beneficiaries living in the 37 states where the federal government is running the markets would lose their subsidies.

Two independent estimates say about 8 million people would drop coverage in a chain reaction that would also send premiums zooming.