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WASHINGTON (USA Today) -- President Obama said Thursday that Americans can keep canceled health insurance policies for a year as companies and consumers adjust to the new demands of the health care law.

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"Americans whose plans have been canceled can choose to re-enroll," the president said during a White House news conference.

In the coming weeks, insurance companies must also notify customers of what those policies lack, and of options consumers have for better coverage under the new law, Obama said. He said, "this fix won't solve every problem, but it will help a lot of people."

The president responded to criticism from lawmakers and Americans who have received cancellation notices since the Obamacare law came on line last month, a period also marred by a malfunctioning website.

After seeing his approval ratings fall in recent weeks, Obama said he knows he has to "win back some credibility" because of problems with the health care law.

"We fumbled the roll-out," said Obama, who also noted at one point: "I was not informed directly that the website was not working correctly."

Administration officials have said policies have been canceled because they do not comply with new coverage requirements prescribed by Obamacare and that the new system offers consumers better, higher quality options.

Obama also indicated he would oppose a House Republican plan that would let people keep their plans for longer, saying it would undercut the structure of the Affordable Care Act.

House Speaker John Boehner, R-Ohio, reacting to news reports of the extension, said, "I'm highly skeptical they can do this administratively," but he awaited the details.

Senate Minority Leader Mitch McConnell, R-Ky., said Obama's statement represented "the clearest acknowledgment yet that his oft-repeated pledge 'if you like your plan, you can keep it' was false all along."

Kaiser Family Foundation senior fellow Karen Pollitz says giving everyone another year to keep their plans and better understand their options is a "reasonable response" by the president.

"If people have the option to renew the policy for another year and if they're also informed about their new options and limitations of their current policies, they can decide their own timing for a transition," says Pollitz. "If they'll be better off moving this open season to ACA market (on Jan. 1) they can; if they decide it makes more sense to wait, they can do that too."

Obama and his signature health care law have come under sharp attack from lawmakers and people who have lost their insurance since the new law came on line last month, or have been unable to log into the website.

Fellow Democrats have been urging Obama to make changes, and a number of bills are making their way through Congress.

Obama's announcement comes a day after the administration announced that only 26,794 people have been able to enroll in Obamacare because of the balky website.

All told, there were some 106,000 sign-ups in October, including about 79,000 who enrolled in 14 states that have their have their own websites, all number lower than projected.

The health care problems appear to be taking a toll on Obama's popularity and approval ratings.

A Quinnipiac Poll this week said that "for the first time" a majority of Americans -- 52% to 44% -- say that Obama is not honest and trustworthy.

"His previous lowest marks on honesty were May 30, when 49% of voters said he was honest and 47% said he wasn't," Quinnipiac reported.

Administration officials, noting that Congress has an even lower approval rating, said voters are upset with all of Washington.

White House spokesman Jay Carney said the president is working to fix problems with the health care law, and other challenges facing Americans.

"We need to focus here on getting the work done that the American people sent us to do," Carney said.

During his health care news conference, Obama said: "We are going to solve those problems. We are going to get this rught, and the Affordable Care Act is going to work."