WASHINGTON — President Obama's plan to help millions of consumers facing health insurance cancellations calmed Democrats on Capitol Hill on Thursday even as its practical effect appeared unclear.

The decision could give some consumers who like their health plans the chance to keep them into 2015, allowing the president to say he honored his pledge that his health law would not force Americans to give up their coverage.

"This fix won't solve every problem for every person," the president said in remarks at the White House, in which he took responsibility for the law's botched rollout. "But it's going to help a lot of people."

Obama's decision appeared to tamp down a rebellion among Democrats worried about a backlash over the Affordable Care Act in next year's election. But some prominent Democrats are still pressing for a more substantive legislative fix.

Public support for the law, which was never robust, has faltered in the wake of the policy cancellations and the debut of the flawed federal online insurance marketplace.

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Republicans, meanwhile, accused Obama of once again selectively enforcing the law, just as he did by delaying enforcement of a requirement that large employers provide health benefits.

How many consumers will actually benefit from Obama's new plan seems likely to vary widely from state to state. Many still may not get the chance to renew.

The plan gives insurance companies federal permission to renew policies that otherwise would be canceled because they do not meet the law's standards. But it does not require companies to renew the policies. Moreover, companies will need the permission of state insurance regulators to act.

Some insurance companies and state officials appear unwilling to do this, although others appeared to be ready to go along with Obama's plan.

Officials at Covered California, which operates the state's marketplace and would have to sign off on the renewal of any current plans, signaled interest in implementing the president's decision.

"Covered California understands the urgent need for clarity around this segment of policy and is working closely with health plans, regulators and policy makers to quickly determine how the president's new guidance will be fulfilled for Californians," spokeswoman Lizelda Lopez said.

Health Care Service Corp., which operates Blue Cross Blue Shield plans in five states including Illinois and Texas, said it would "comply with any new requirements" and contact consumers "who will have new options as a result of this announcement."

Insurance officials in Illinois said they were assessing Obama's plan.

But regulators in several states, including Arkansas and Washington, said they would not renew plans beyond next year.

And the National Assn. of Insurance Commissioners expressed strong reservations about the proposal.

Obama's plan would suspend enforcement of a provision in the law that requires health plans sold after Jan. 1 to meet new basic requirements, such as providing coverage for prescription drugs, hospitalizations and maternity care. Many current plans don't include all these benefits.

But many states have already enacted their own laws and regulations codifying these requirements.

"This could get kind of sticky in a number of states," said Timothy Jost, a health law expert at Washington and Lee University School of Law and a supporter of the 2010 healthcare law.

In California, the industry's state association blasted the president's plan.

"California needs to stay the course and transition people into the more comprehensive policies that meet the requirements of the Affordable Care Act," said Patrick Johnston, president of the California Assn. of Health Plans. "Consumers could see rate increases for extended policies that won't have the added value of ACA required benefits. And the exchange would be unbalanced with a pool of older, sicker people, causing additional increases in rates."

The administration had hoped the online marketplaces that opened Oct. 1 would give consumers attractive alternatives to their current coverage. But the flawed healthcare.gov website has prevented millions of potential shoppers from even seeing what kind of plan they could get next year.

"We fumbled the rollout of this healthcare law," Obama said, identifying the website and the cancellations as "two fumbles."

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"That's on me," he said, regarding the cancellation letters that millions of consumers have received. "That's something I deeply regret, because it's scary getting a cancellation notice."

He also took pains to assume responsibility for the problems, saying the public should blame him, not members of Congress who have repeated his statements that Americans could keep health plans they liked.

"They were making representations based on what I told them and what this White House and our administrative staff told them, and so it's not on them, it's on us," he said. "But it is something that we intend to fix."

Those words were designed, in part, to quell a revolt among Democrats on Capitol Hill who threatened to buck the White House and back legislation that would extend even more current health plans into next year and beyond.

House Republicans planned to vote on one such plan Friday.

White House aides dispatched to Capitol Hill to sell the president's alternative Thursday received a warmer reception than they did earlier in the week, Democratic lawmakers said. Some emerged from the meeting saying the plan had addressed their concerns, although some skeptics remained undecided about the GOP bill.

"I'm keeping open on it," said Rep. Nick J. Rahall II, a West Virginia Democrat who is expecting a tough reelection fight. Rahall said he had questions about how the fix would work and whether it would reassure his anxious constituents. "How will they have a peace of mind that these letters were wrong, that they can keep what they have? Will they get a follow-up letter? Will they be given options?"

Comments from House Speaker John A. Boehner (R-Ohio) that Republicans were not interested in fixing the law also appeared to dissuade Democrats from backing the GOP bill.

"The only way to fully protect the American people is to scrap this law once and for all," Boehner said in a news conference at the Capitol. "There is no way to fix this."

Several Democrats still want to vote on the issue as a way to telegraph to their constituents that they are listening to their concerns and standing up to the president.

Sen. Mary Landrieu (D-La.), who drafted a bill that was gaining support among Democrats, said after the president's announcement that she was "encouraged" but would continue to push her bill.

"We will probably need to make a legislative fix," she said.

noam.levey@latimes.com

kathleen.hennessey@latimes.com

michael.memoli@latimes.com

Peter Frost in Chicago, Lisa Mascaro and Christi Parsons in the Washington bureau, and Chad Terhune in Los Angeles contributed to this report.