WASHINGTON — Bowing to pressure, President Barack Obama on Thursday announced changes to his health care law to give insurance companies the option to keep offering consumers plans that would otherwise be canceled.

The administrative changes are good for just one year, though senior administration officials said they could be extended if problems with the law persist. Obama announced the changes at the White House.

“This fix won’t solve every problem for every person, but it’s going to help a lot of people,” the president said.

He acknowledged that “we fumbled the rollout of this health care law” and pledged to “just keep on chipping away at this until the job is done.”

He also promised to work to regain the trust of the American people.

“I think it’s legitimate for them to expect me to have to win back some credibility on this health care law in particular and on a whole range of these issues in general,” he said.

Obama has been under enormous pressure from congressional Democrats to give ground on the cancellation issue under the health care overhaul, a program likely to be at the center of next year’s midterm elections for control of the House and Senate.

It’s unclear what the impact of Thursday’s changes will be for the millions of people who have already had their plans canceled. While officials said insurance companies will now be able to offer those people the option to renew their old plans, companies are not required to take that step.

The main industry trade group, America’s Health Insurance Plans, said Obama’s offer comes too late and could lead to higher premiums, since companies already have set 2014 rates based on the assumption that many people with individual coverage will shift over to the new markets created under Obama’s law.

Karen Ignagni, president of the industry group, didn’t speculate on whether companies would extend coverage for those threatened with cancellation, but warned in a statement that “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.”

Insurance companies will be required to inform consumers who want to keep canceled plans about the protections that are not included under those plans. Customers will also be notified that new options are available offering more coverage and in some cases, tax credits to cover higher premiums.

Under Obama’s plan, insurance companies would not be allowed to sell coverage deemed subpar under the law to new customers, marking a difference with legislation that House Republicans intend to put to a vote on Friday.

Only last week, Health and Human Services Secretary Kathleen Sebelius told a Senate panel she doubted that retroactively permitting insurers to sell canceled policies “can work very well since companies are now in the market with an array of new plans. Many have actually added consumer protections in the last three-and-a-half years.”

Republicans were unimpressed with the changes.

House Speaker John Boehner, speaking in advance of the president’s announcement, insisted it was time to “scrap this law once and for all.”

“You can’t fix this government-run health care plan called Obamacare ,” he said. “It’s just not fixable.”

Obama, for his part, made clear he would continue to fight ongoing attempts to sink the whole program, saying, “I will not accept proposals that are just another brazen attempt to undermine or repeal the overall law and drag us back into a broken system.”

“We’re going to solve the problems that are there, we’re going to get it right, and the Affordable Care Act is going to work for the American people,” he pledged.

While the White House deals with the cancellation issue, the administration is also promising improvements in a federal website so balky that enrollments totaled fewer than 27,000 in October in 36 states combined. The administration had said in advance the enrollment numbers would fall far short of initial expectations. After weeks of highly publicized technical woes, they did.

Adding in enrollment of more than 79,000 in the 14 states with their own websites, the nationwide number of 106,000 October sign-ups was barely one-fifth of what officials had projected – and a small fraction of the millions who have received private coverage cancellations as a result of the federal law.

The administration said an additional 1 million people have been found eligible to buy coverage in the markets, with about one-third qualifying for tax credits to reduce their premiums. Another 396,000 have been found eligible for Medicaid, which covers low-income people.

Administration officials and senior congressional Democrats expressed confidence in the program’s future. “We expect enrollment will grow substantially throughout the next five months,” said Sebelius, who is in charge of the program.

“Even with the issues we’ve had, the marketplace is working and people are enrolling,” she added.

Despite the expressions, the White House worked to reassure anxious Democrats who are worried about the controversial program, which they voted into existence three years ago over Republican opposition as strong now as it was then.

Obama said he regretted the political grief he’d caused members of his own party who’d backed him on the health care law.

“There is no doubt that our failure to roll out the Affordable Care Act smoothly has put a burden on Democrats, whether they’re running or not, because they stood up and supported this effort through thick and thin,” he said.

Senate Democrats arranged a closed-door meeting for midday Thursday in the Capitol with White House officials, who held a similar session Wednesday with the House rank and file. Ahead of that meeting, Obama planned to speak from the White House about new efforts to help Americans receiving insurance cancellation notices.

So far, five Senate Democrats are on record in support of legislation by Sen. Mary Landrieu, D-La., to make sure everyone can keep their present coverage if they want to. The bill would require insurance companies to continue offering existing policies, even if they fall short of minimum coverage requirements in the law.

The measure has little apparent chance at passage, given that it imposes a new mandate on the insurance industry that Republicans will be reluctant to accept.

At the same time, a vote would at least permit Democrats to say they have voted to repair some of the problems associated with the Affordable Care Act, as many appear eager to do.

In a statement, Landrieu said Sens. Jeff Merkley of Oregon, Kay Hagan of North Carolina and Mark Pryor of Arkansas were now supporting the legislation, as is Sen. Dianne Feinstein of California. All but Feinstein are on the ballot next year.

Across the Capitol, majority Republicans in the House set a vote for Friday on legislation to permit insurance companies to continue selling existing policies that have been ordered scrapped because they fall short of coverage standards in the law.

While House passage of the measure is assured, each Democrat will be forced to cast a vote on the future of a program that Republicans have vowed to place at the center of next year’s campaign.

Democratic Rep. Mike Doyle of Pennsylvania, who voted for the initial Obama health care bill, said Thursday that members of his caucus want an opportunity to go on the record in support of allowing people to keep the insurance they had.

Doyle told MSNBC in an interview that at a White House meeting Wednesday, House Democrats told Obama about “the frustration level that many of us have” with the health care roll-out.

Doyle said Democrats warned Obama that “if you don’t give us something by Friday” to fix the insurance cancellation problem, then many Democrats are likely to vote for the pending House bill sponsored by Republican Rep. Fred Upton of Michigan, which would accomplish that goal.

The promise of keeping coverage was Obama’s oft-stated pledge when the legislation was under consideration, a calling card since shredded by the millions of cancellations mailed out by insurers.

Obama apologized last week for the broken promise, but aides said at the time the White Hous