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.