In an effort to head off a Democratic revolt, President Obama announced a fix to the Affordable Care Act Thursday that would let Americans keep their insurance plans for one year if they choose to.

A contrite Obama repeatedly took responsibility for the botched rollout of the law, and delivered a message to Americans who have complained about receiving cancellation notices: ”I hear you loud and clear.” On more than one occasion, the president said he and his administration “fumbled” the rollout of the law.

The fix would let people whose policies have been cancelled because they don’t meet Obamacare’s standards renew those policies, smoothing the transition to the insurance exchanges. It would also require insurance companies to tell people re-enrolling that their plans don’t meet the ACA’s requirements, and to give information about better options.

“Already people who have plans that predate the Affordable Care Act can keep those plans if they haven’t changed. That was already in the law,” Obama said. “Today we’re going to extend that principle both to people whose plans have changed since the law took effect and people who bought plans since the law took efffect.”

But the president reiterated that he would resist efforts aimed not at fixing but at weakening the ACA, a reference to a House Republican proposal, scheduled to receive a vote Friday, that experts say would fatally damage the law.

“I will not accept proposals that are a brazen attempt to undermine the law,” Obama said, adding: “I’m not going to walk away from 40 million Americans who can get health insurance for the first time.”

Hundreds of thousands of Americans have seen their insurance cancelled despite repeated promises from Obama that those who liked their insurance could keep it.

Crucially, Obama’s proposed change doesn’t require approval from lawmakers. Given Republican control of the House, the chances of getting any constructive fixes to the ACA through Congress are slim to none.

House Speaker John Boehner issued a statement calling the move “little more than a political response designed to shift blame rather than solve the problem.”

And Sen. Ted Cruz, the Texas Republican who has been the law’s most prominent critic, said in a statement: “We cannot ‘fix’ Obamacare. The damage has been done, as millions of Americans have already been made to pay higher premiums and lose their jobs, wages, and health care plans.”

Obama offered his proposal amid growing warnings from House Democrats—spooked by the politial fallout over the botched rollout— that without a fix, they might be forced to support the Republican proposal scheduled for a vote Friday. The measure, sponsored by Rep. Fred Upton of Michigan, would let insurers continue to offer sub-standard plans through 2014.

At a meeting Wednesday, House Democrats reportedly “upbraided” administration officials for the political problems created by Obama’s pledge that people could keep their insurance.

“I want to find out what they are wanting to do,” Rep Ron Barber, an Arizona Democrat, said Wednesday, NBC reported. “If they can do something that makes sense and can fix the problem then that’s one thing, but if they can’t clearly the Upton bill can be an option for me.”

The White House is anxious to head off Democratic support for the Upton bill, believing it could do mortal damage to Obama’s signature legislative accomplishment. By allowing insurers to continue selling sub-standard plans through next year to new customers, Upton’s bill would undermine the entire set-up for the health exchanges in the first crucial year of operation.

In an interview Wednesday with MSNBC, Jonathan Gruber, the M.I.T. economics professor who helped design the law, as well as the similar Massachusetts law pushed by Mitt Romney, called Upton’s bill “an unmitigated disaster” that’s “designed to undo the entire law.” That’s because it’s impossible to reform the private health insurance market without making a small number of people pay more, Gruber explained.

Obama acknowledged Thursday that the fiasco “has put a burden on Democrats, whether they’re running or not.”

He added: “They supported this effort through thick and thin. And you know I feel deeply responsible for making it harder for them rather than easier for them to continue to promote the core values that I think led them to support this thing in the first place.”

But whether Obama’s proposal will be enough to avoid a Democratic rebellion remains to be seen. It’s not clear whether insurers will choose to continue the dropped plans, or how they’ll be able to reinstate them.

America’s Health Insurance Plans, the industry’s top lobbying group, met Obama’s remarks with criticism.

“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,” the group’s president and CEO, Karen Ignagni, said in the statement. “Premiums have already been set for next year based on an assumption of when consumers will be transitioning to the new marketplace. 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. Additional steps must be taken to stabilize the marketplace and mitigate the adverse impact on consumers.”

Majority Leader Harry Reid applauded the president’s remarks. ”Republicans should stop listening to the extremist voices in their party who only want to repeal the benefits of the Affordable Care Act,” he said. “Whenever Republicans decide to stop rooting for failure, roll up their sleeves and get to work, we stand ready and willing to work with them and find common ground.”

He said Republicans “want to go back to the days when insurance companies could deny people coverage for pre-existing conditions, treat being a woman as pre-existing condition, and watch health care costs drive families into bankruptcy.”