President Obama defended his health-care law during a long question and answer session about the Affordable Care Act Friday. “I'm not going to walk away from 40 million people who have the chance to get health insurance for the first time," he said. (The Washington Post)

President Obama relented to pressure from the public and his own party Thursday and changed one of the bedrock requirements of the new health-care law to fulfill his promise to allow people to keep their insurance plans if they want.

While the move was aimed at solving a problem that was threatening the president’s credibility and public faith in the law, it raised a slew of new questions, including whether insurers would adjust, whether millions of customers would pay higher premiums and whether states would make the fix available.

The president made the change at a White House news conference that quickly turned from a specific policy announcement into a nearly hour-long deconstruction of broader flaws with the health-care law and Obama’s responsibility for its early failures.

The president was contrite, and his admissions were many — he conceded that he was left in the dark about aspects of the crowning achievement of his presidency, he acknowledged that he and his advisers underestimated how hard it would be to sell insurance over a Web site, he could not guarantee that the site would work well for everyone by the end of the month, he allowed that federal government rules were an impediment, and he lamented the political problems he caused for members of his party.

“There have been times where I thought we were . . . slapped around a little bit unjustly. This one’s deserved, all right? It’s on us,” Obama said regarding the policy cancellation issue, which contradicted his repeated promises that people would be able to keep insurance plans they liked.

Who has been able to select a health-care plan

Obama said insurance companies could continue for another year to offer health plans sold to individuals and small businesses that do not meet requirements under the new law that set minimum standards for the benefits that policies must cover.

Individual policies have long been a problematic part of the insurance market, with higher prices than most group plans, fewer benefits and a tendency to cut off people when they get sick. The health-care law tried to address this problem by directing Americans who rely on individual policies to buy coverage through the new insurance marketplaces — and by defining the set of essential benefits.

Under the new rules, people may renew individual and small-group policies, which otherwise would have ended with the new year, until Oct. 1 — allowing them to stay in effect through September 2015. Obama said the administration will insist that insurance companies that continue to sell policies that do not comply with the new law inform consumers about “what protections these renewed plans don’t include” and alert customers to potentially better and more affordable insurance in the new federal and state marketplaces.

The president’s remarks came as a number of recent polls illuminated the escalating problems that Obama and Democrats face. A new Gallup poll released Thursday shows that disapproval of the Affordable Care Act has risen from 47 percent just a couple of weeks ago to a high of 55 percent. At the same time, Obama’s approval ratings have dropped, hovering between the high 30s and low 40s.

The new proposal appeared to strengthen the president’s position with Democratic lawmakers, including those in the House who will vote Friday on a Republican bill that would let people keep their existing policies for a year and also allow new customers to buy them even though they don’t conform to the new law.

“For now, the president’s actions are sufficient,” Rep. Elijah E. Cummings (Md.), the top Democrat on the House Oversight and Government Reform Committee, told reporters after a nearly 90-minute briefing with White House Chief of Staff Denis McDonough.

Not all House Democrats were convinced. Rep. Kyrsten Sinema (Ariz.) said that the plan is “a start” but that she will vote for the Republican proposal.

In his news conference, Obama described the Oct. 1 launch of the federal health insurance marketplace as “rough” and cautioned that the online enrollment system that has been plagued by glitches may not be fully fixed by the end of the month, which was the target date.

Obama described the cancellations on the individual market and the Web site’s rollout as “two fumbles . . . on a big game — but the game’s not over.” He vowed that the nation will not return to what he called the broken health-care system that existed before the Affordable Care Act.

For some, the president’s announcement raised more questions. Deborah Persico, a 58-year-old D.C. lawyer who represents indigent criminal defendants, received a letter saying her plan would be canceled in October 2014. She’s not sure whether the president’s “fix” will mean her plan will be extended through January 2015, and in any event, she would still have to shop on the city’s new health insurance exchange, where a comparable plan comes with a higher premium, higher deductible and higher out-of-pocket cost.

“It’s just a temporary delay of the inevitable. You’re still going to lose your policy,” she said. “A fix would have been ‘If you like your policy, you can keep your policy, period.’ This is just ‘If you like your policy, you can keep your policy for a year.’ ”

Though the president announced the change, the White House is allowing each state to determine whether its residents may keep non-compliant health plans. State insurance commissioners and other health policy experts made clear that the landscape will vary substantially around the country.

Eight states, including California and New York, have recently forbidden insurance companies to continue to sell individual or small-group health plans unless they meet the new federal standards for coverage.

Within hours of the president’s announcement, Washington’s insurance commissioner issued a defiant statement that criticized the president and said the state will not allow non-compliant policies to be extended beyond the end of the year.

“I do not believe his proposal is a good deal for the state of Washington,” said the insurance commissioner, Mike Kreidler, adding that substandard health plans need to end in order to protect consumers and prevent prices from rising.

Arkansas’ insurance commissioner, Jay Bradford, said he will not permit the extension. “It would be more chaos added to an already chaotic situation,” he said.

In the Washington region, Care­First, the area’s dominant carrier, said it is studying Obama’s announcement and will communicate directly with affected policyholders. But CareFirst noted that it is “strictly bound” by state laws. “At the moment, it is unclear whether state laws would preclude us from doing what the president has proposed,” CareFirst said.

In Maryland, for example, state law requires that beginning in 2014, new plans in the individual and small-group market meet the provisions of the Affordable Care Act, including coverage of essential health benefits, such as maternity care.

Officials in Florida and Kentucky said they will heed the president’s call to grant extensions.

Insurers said Thursday that although they appreciate Obama’s effort to address consumer concerns, they remain worried that the move could distort the risk pool in the new state and federal health insurance marketplaces. That’s because individual policies tend to be significantly more expensive than group insurance, except for customers who are young, healthy and use little medical care — the very people whom federal officials are counting on to join the new exchanges.

“Changing the rules after health plans have already met the requirements of the law could destabilize the market and result in higher premiums for consumers,” said Karen Ignani, president and chief executive of America’s Health Insurance Plans. “If now fewer younger and healthier people choose to purchase coverage in the exchange, premiums will increase and there will be fewer choices for consumers.”

The American Academy of Actuaries was among the groups that immediately warned of negative effects. The White House’s approach is “threatening the viability” of the new insurance marketplaces, said Corri Uccello, the academy’s senior health fellow.

Even if their mix of customers changes as a result of the new rules, insurers cannot change their prices for 2014, because the rates already have been set by each state’s insurance regulators. Senior administration officials said they could not predict what might happen to prices for 2015, when some old individual and small-business policies will still be in effect for much of the year.

Jackie Kucinich, Sarah Kliff and Paul Kane contributed to this report.