Following weeks of public outrage, President Barack Obama on Thursday relented to political pressure and said that health insurance companies could renew for another year the policies of millions of Americans that insurers had previously canceled.

The news was greeted with glee by those facing steep premium hikes because their policies do not comply with the president’s health care law. “This fix won’t solve every problem for every person, but it’s going to help a lot of people,” the president said.

Still, Obama’s announcement at a White House news conference seemed to create more confusion than clarity.

It wasn’t immediately known how many states and insurers will go along with Obama’s “administrative action.” And insurance companies and health care economists warned that many policyholders may face much higher rates in 2015 as a result of the yearlong reprieve.

But it was hard to ignore the widespread — if only temporary — relief of those who are facing skyrocketing insurance rates as they are being forced to buy new policies that include the law’s 10 standard benefits, such as mental health and maternity care. Many policyholders could readily quote Obama’s oft-repeated promise that “if you like your plan, you can keep it,” only to open their mail to discover that wasn’t the case.

Brian Okamoto, a 57-year-old San Jose resident, said the president’s action surprised him “because I thought he would just go full-speed ahead and wouldn’t try to put together a one-off special plan for one circumstance.”

Okamoto said his $446 monthly premium and $2,600 yearly deductible is now set to climb to $630 monthly, with a $3,500 deductible — the best deal he could find on the state’s new online insurance exchange.

“For me, it’s reassuring that if the president believes he did something wrong, he’s trying to fix it,” Okamoto said.

Obama’s action allows insurers to renew the individual policies that don’t include the standard benefits. The action also requires insurers to inform about 5 million consumers about their options, which could include buying a better plan on one of the online marketplaces. The president left the decision up to state insurance commissioners — and some on Thursday balked, including those in Oregon and Washington state.

But California’s insurance commissioner, Dave Jones, said that he will ask all health insurers in California to do as Obama requested and allow their customers to stay on their current policies through the end of 2014.

Jones, however, noted that of the 1.1 million Californians who had their policies canceled, many should be able to find a better deal on the state’s online exchange, Covered California. He said at least 300,000 of those people are now eligible for federal subsidies.

Patrick Johnston, president and CEO of the California Association of Health Plans, a trade group that represents 42 health insurers, warned that Obama’s action would cause “significant disruption in the marketplace.” He said consumers in the individual insurance market could expect to see rate increases for policies extended into 2014 that would not have the “added value” of policies that comply with the law.

And with hundreds of thousands of Californians removed from the “risk pool,” the exchange would be “unbalanced with a pool of older, sicker people, causing additional increases in rates,” Johnston said.

Jay Bhattacharya, a health care economist who is an associate professor of medicine at Stanford, said Johnston is not crying wolf.

“The exchange needs relatively healthy people to sign up for plans so you could have reasonable premiums,” he said. But Obama’s action “keeps lots and lots of relatively healthy people off the exchange.”

Obama’s plan sparked a Capitol Hill frenzy Thursday.

Most Republicans rejected it outright. “This problem cannot be papered over by another ream of Washington regulations,” said House Speaker John Boehner, R-Ohio, who urged support for a bill by Rep. Fred Upton, R-Mich.

The bill would not only let people with insurance that doesn’t meet the new law’s standards keep it through 2014, but it would also let new customers buy such policies too — a nonstarter for most Democrats.

On Thursday, Democrats rushed between meetings in search of consensus as opinions changed almost by the hour.

Rep. George Miller, D-Martinez, said early Thursday afternoon that a one-year delay would send premiums skyrocketing. “Congress, in its panic, is taking everyone out of the pool and making it more difficult to have rates that are affordable,” he said.

But Miller’s staff a short while later said that he, too, was considering support of the yearlong delay. Asked about the premium spikes Miller had described less than two hours earlier, chief of staff Daniel Weiss replied that the congressman was “still working on that part.”

U.S. Sen. Dianne Feinstein, D-Calif., praised Obama “for responding quickly and providing the necessary flexibility” but said she’s still co-sponsoring a bill by Sen. Mary Landrieu, D-La., to require insurers to indefinitely keep offering all individual policies that existed this year.

“Changing health insurance plans is deeply personal, and I believe it should be up to individuals to make that choice,” she said. “That was the intent of the law, and it is how I believe it should be run going forward.”

In San Leandro, small business consultant Linda Entrikin agreed, saying she was thrilled with the news.

Entrikin, 62, supports the health law but doesn’t understand why her plan needs to be canceled and replaced with one that she says is similar but more expensive.

“I don’t think you should be penalizing the people who have been doing the right thing all along and buying insurance,” Entrikin said.

Administration officials had labeled many of the individual plans “junk insurance” because they lack basic coverage. But Entrikin rattled off a list of benefits on her current Kaiser policy that closely matches the plans offered on the insurance exchange.

Her current Kaiser policy, for which she pays $399 a month, would jump to $608 — even if she went with the cheapest plan available to her on the online insurance marketplace.

“I knew something had to give,” she said, “and now that’s happened. Yay!”