The poll comes with about 60 days left in open enrollment season. The administration is playing catch-up to meet its goal of signing up 7 million people in new insurance exchanges that offer subsidized private coverage to middle-class households. So far, the markets have attracted an older crowd that tends to be more costly to cover. Younger people in the coveted 18-34 age group are still mainly on the sidelines.
While the poll did not find a turnaround for Obamacare, the trend offers some comfort for supporters of the health care law.
In December, 76 percent of adults had said the opening of the new markets was not going well. Such negative perceptions have now fallen 10 points to 66 percent.
Still, rave reviews remain rare.
(Read more: GOP seeks own policy cure to replace Obamacare)
Only 4 percent said things were going extremely or very well, while another 17 percent said things were going somewhat well.
Compare that to 38 percent who said the rollout had gone not at all well. Another 28 percent said things were not going too well. Add those together and it makes up two-thirds of the public.
"People were locked out of the system," said Karyle Knowles, a restaurant server from San Antonio. "They weren't able to access what they should have, which only added to the mayhem."
The White House had hoped to bring the ease of online shopping to the daunting process of buying health insurance. Instead, the federal website serving 26 states froze up when it was launched Oct. 1. Some of the 14 states running their own sites also encountered problems. It took the better part of two months to straighten out the issues with the federal exchange.
The administration reported Friday that 3 million people have now signed up for private coverage through federal and state markets, and another 6.3 million have been deemed eligible for Medicaid coverage. It's not clear how many of those were previously uninsured.
According to the poll, many website users have had a frustrating experience. Among those who've tried to sign up, just 8 percent say it worked well, 29 percent somewhat well, 53 percent not well.
(Read more: Medicaid enrollment jumps—but is it Obamacare?)
The public's take on the law itself is stable, with 27 percent saying they back it, 42 percent opposed and 30 percent neutral. Those figures are unchanged since December.
People who have tried to sign up are more positive than the overall public—46 percent say they back the law, 31 percent oppose it.