WASHINGTON — Despite a late surge in sign-ups, support for President Barack 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 Yet even fewer — 13 percent — think it will be completely repealed.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“To get something repealed that has been passed is pretty impossible,” said Gwen Sliger of Dallas.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 Forty-one percent said it should be completely repealed, about double the 19 percent who said it should remain in the law as passed.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.

The only part of the law that seems immune to changes is an early provision allowing young adults to stay on their parents’ plan until they turn 26. Fifty-one percent said it should remain as passed.

The poll suggests that even the popular ban on insurers denying coverage to people with pre-existing medical conditions could be tweaked. While 39 percent said it should remain as passed, 43 percent wanted to keep it with changes.

Larry Carroll, 64, a church deacon from Cameron, W.Va., says he’s strongly opposed to the health care law, but doesn’t have high hopes for repeal.

“The federal bureaucracy simply seems to be too strong,” he said. “The federal bureaucracy is like an anaconda.”

Teresa Stevens, a factory supervisor from Jacksonville, Fla., said her two adult sons shopped for coverage on the health insurance exchanges and found it too expensive.

“There are so many different things they say about (the law) that are not true,” she said. “It’s not affordable.”

A supporter of former Democratic President Bill Clinton, Stevens said the economy has soured for working people under Obama. “Everything is so expensive, not just health care,” she said.

The poll found that much of the slippage for the health care law over the last four years has come from a drop in support, not an increase in opposition.

In April of 2010, soon after the law passed, 50 percent of Americans said they were opposed to it, while 39 percent were in favor.

Now, just 26 percent say they are in favor, a drop of 13 percentage points. Forty-three percent say they are opposed, a drop of 7 percentage points since four years ago.

The AP-GfK Poll was conducted March 20-24 using KnowledgePanel, GfK’s probability-based online panel designed to be representative of the U.S. population. It involved online interviews with 1,012 adults and has a margin of sampling error of plus or minus 3.4 percentage points for all respondents.

Respondents were first selected randomly using phone or mail survey methods and were later interviewed online. People selected for KnowledgePanel who didn’t otherwise have access to the Internet were provided with the ability to access the Internet at no cost to them.