Ahead of a vote on repeal in the GOP-led House this week, strong opposition to the law stands at 30 percent, close to the lowest level registered in AP-GfK surveys dating to September 2009.
The nation is divided over the law, but the strength and intensity of the opposition appear diminished. The law expands coverage to more than 30 million uninsured, and would require, for the first time, that most people in the United States carry health insurance.
The poll finds that 40 percent of those surveyed said they support the law, while 41 percent oppose it. Just after the November congressional elections, opposition stood at 47 percent and support was 38 percent.
As for repeal, only about one in four say they want to do away with the law completely. Among Republicans support for repeal has dropped sharply, from 61 percent after the elections to 49 percent now.
Also, 43 percent say they want the law changed so it does more to re-engineer the health care system. Fewer than one in five say it should be left as it is.
"Overall, it didn't go as far as I would have liked," said Joshua Smith, 46, a sales consultant to manufacturers who lives in Herndon, Va. "In a perfect world, I'd like to see them change it to make it more encompassing, but judging by how hard it was to get it passed, they had to take whatever they could get."
His extended family has benefited from the law. A sister-in-law in her early 20s, previously uninsured, was able to get on her father's policy. "She's starting out as a real estate agent, and there's no health care for that," said Smith. The law allows young adults to stay on a parent's plan until they turn 26.
Congress stepped back last week to honor victims of the rampage in Tucson, Ariz., that left Rep. Gabrielle Giffords, D-Ariz., facing a long and uncertain recovery from a bullet through her brain.
There's no evidence the gunman who targeted Giffords was motivated by politics, but the aftermath left many people concerned about the venom in public life. A conservative Democrat, Giffords had been harshly criticized for voting in favor of the health overhaul, and won re-election by a narrow margin.
House Republican leaders say they're working to keep this week's debate - and expected vote Wednesday - from degenerating into a shouting match, but it depends on the Democrats, too. Republicans want a thoughtful discussion about substantive policy differences, said Brad Dayspring, a spokesman for Rep. Eric Cantor, the No. 2 GOP leader. The AP-GfK poll was under way when the attack in Tucson took place Jan. 8.
Opposition to the law remains strongest among Republicans. Seventy-one percent of them say they're against it, as compared with 35 percent of independents and 19 percent of Democrats. Republicans won back control of the House partly on a promise to repeal what they dismissively term as "Obamacare."
"I just think that the liberal left is more going for socialized medicine, and I don't think that works well," said Earl Ray Fye, 66, a farmer from Pennsylvania Furnace, Pa., and a conservative Republican. "It just costs too much. This country better get concerned about getting more conservative."
One of the major Republican criticisms of the law found wide acceptance in the poll, suggesting a vulnerability that GOP politicians can continue to press.
Nearly six in 10 oppose the law's requirement that people carry health insurance except in cases of financial hardship. Starting in 2014, people will have to show that they're covered either through an employer, a government program, or under their own plan.
Rich Johnson, 34, an unemployed laborer from Caledonia, Wis., said he thinks the heart of the law is good. "The problem I have with it is mandating insurance so that you have to have it or you'll get fines," said Johnson, an independent. "I just don't think people should be forced to have it. The rest of it, I have no problem with."
The individual mandate started out as a Republican idea during an earlier health care debate in the 1990s. More recently, Massachusetts enacted such a requirement under GOP Gov. Mitt Romney and the Democratic Legislature. Nowadays, most conservatives are against it, and GOP state attorneys general are suing to have the mandate overturned as unconstitutional.
Other major provisions of the law, including a requirement that insurers accept people with pre-existing medical conditions, got support from half or more of the public in the poll.
Loralyn Conover, 42 a former music teacher with multiple sclerosis, says she hopes repeal goes nowhere. Senate Democrats say they'll block it.
The new law "opens the door for people like me to have some kind of pay-as-you-go health insurance," said Conover, of Albuquerque, N.M. "It's nice to be able to have something . and not be dropped in the cracks of society." She couldn't get health insurance when she was first diagnosed, but is now covered by Medicare.
The AP-GfK Poll was conducted Jan. 5-10 by GfK Roper Public Affairs and Corporate Communications. It involved landline and cell phone interviews with 1,001 adults nationwide, and has a margin of sampling error of plus or minus 4.2 percentage