WASHINGTON — Despite a late surge in sign-ups, support for President Obama’s health care law is languishing at its lowest level since passage of the landmark legislation four years ago, according to a new poll.

The Associated Press-GfK survey finds that 26 percent of Americans support the Affordable Care Act. Yet even fewer – 13 percent – think it will be completely repealed. A narrow majority expects the law to be further implemented with minor changes, or as passed.

“To get something repealed that has been passed is pretty impossible,” said Gwen Sliger of Dallas. “At this point, I don’t see that happening.”

Sliger illustrates the prevailing national mood. Although a Democrat, she’s strongly opposed to Obama’s signature legislation. Yet she thinks “Obamacare” is here to stay.

“I like the idea that if you have a pre-existing condition you can’t be turned down, but I don’t like the idea that if you don’t have health insurance you’ll be fined,” said Sliger.

That central requirement that virtually all Americans have coverage or face fines remains highly unpopular. Forty-one percent said it should be completely repealed, about double the 19 percent who said it should remain in the law as passed. Obama, insurers, and most policy experts consider the so-called individual mandate essential to creating a big insurance pool that keeps premiums affordable.

The poll was taken before Thursday’s announcement by the White House that new health insurance markets have surpassed the goal of 6 million sign-ups, so it did not register the potential impact of that news on public opinion. Open enrollment season began with a dysfunctional HealthCare.gov website last Oct. 1. It will end Monday at midnight EDT, on what looks to be a more positive note.

Impressions of the coverage rollout while low, have improved slightly.Only 5 percent of Americans say the launch of the insurance exchanges has gone very or extremely well. But the number who think it has gone at least somewhat well improved from 12 percent in December to 26 percent now. The exchanges are marketplaces that offer subsidized private coverage to people without a plan on the job.

Of those who said they or someone in their household tried signing up for coverage, 59 percent said there were problems.

Repealing the health care law is the rallying cry of Republicans running to capture control of the Senate in the fall elections. The Republican-led House has already voted more than 50 times to repeal, defund or scale back “Obamacare,” but has been stymied in its crusade by Democrats running the Senate. Playing defense, Democrats are campaigning with a message of fixing the law to make it work better.

The poll found that 7 in 10 Americans believe the law will be implemented with changes.Forty-two percent think those changes will be minor, and 30 percent say they think major changes are in store.

Combining the 42 percent who see minor changes coming and 12 percent who say they think the law will be implemented as passed, a narrow majority of 54 percent see either tweaks in store, or no changes at all.