WASHINGTON (AP) — Little more than a week after millions of consumers received health care cancellation notices, lawmakers in both parties are pushing legislation to redeem President Barack Obama's long-ago pledge that anyone liking their coverage will be allowed to keep it under the nation's controversial new law.

The result is a stern new challenge for the White House as it struggles to fix website woes for the signup portal for those seeking to enroll under the law, and simultaneously copes with angry consumers who rightly or wrongly blame "Obamacare" for cancellation letters mailed by insurers.

Democratic officials said top administration aides got a close-up view of the cancellation controversy last week, when Sen. Joe Donnelly, D-Ind., said at a closed-door meeting of the party's rank and file that his son had received notice his coverage was being terminated.

In response, these officials said White House Chief of Staff Denis McDonough referred to a speech Obama had made earlier in the week saying some of those losing coverage would qualify under Medicaid, some would receive federal subsidies for individual coverage, and others would have options in the so-called exchanges the law set up to allow individuals to shop for insurance. Donnelly's office declined several requests for comment. The officials who described the incident did so on condition of anonymity, saying they were not authorized to discuss a private meeting.

In the Republican-controlled House, officials say a vote is likely as early as next week on a bill to let insurers continue selling any individual policies that were in effect on Jan. 1, 2013, even if they provide coverage deemed insufficient under Obamacare.

The measure, drafted by Rep. Fred Upton, R-Mich., and backed by roughly 100 fellow Republicans, would remain in effect throughout 2014, after which the issue would presumably be reviewed.

"Despite the president's repeated promise of 'if you like your plan, you can keep it,' many Americans are now learning the sad reality that their current plan will no longer exist beginning on January 1," Upton, chairman of the Energy and Commerce Committee, said in a statement when he announced his legislation last week.

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"This legislation is about providing folks the peace of mind that they will be allowed to keep their current coverage if they so choose."

While Upton's legislation permits insurers to sell existing coverage plans that would otherwise be banned, Sen. Mary Landrieu, D-La., introduced legislation during the day to go one step further by requiring it.

Aides said that under her measure, insurance companies would be obliged to continue offering existing paying customers continued coverage under any plans in effect at the end of 2013. No new consumers could enroll.

"A promise was made that if you like your health plan, you can keep it - and I will do everything I can to see that the promise is kept," said Landrieu, who is gearing up for what is expected to be a challenging re-election campaign next year.

In a statement, Landrieu added that "Many people may find better plans in the marketplaces that offer superior coverage for them at a good value and at a potentially lower cost. But if people want to keep their current plans, they should be able to do so."

Her measure also requires insurers to explain areas in which the coverage falls short of the law's requirements, and notify consumers they may be able to find an alternative plan that meets the requirements.

The White House declined comment on the two bills.

Both measures are designed to cut through a complicated system in which some plans for individuals that fall short of coverage standards are allowed to continue under Obamacare, while others are not.

In general, individual coverage plans in effect on the date the legislation was enacted, March 23, 2010, may continue to be sold, regardless of their coverage levels. There are exceptions, though, including plans that significantly increase costs to consumers through higher deductibles, copayments or other steps.

According to an explanation published by Families USA, an increase in deductibles above medical inflation plus 15 percentage points would disqualify a plan from continued sale, for example.

Under current law, plans that went into effect after March 23, 2010 and fall short of the law's coverage requirements may not be sold beyond the end of the year.

That means that insurance companies that began selling new policies later throughout much of 2010 or in the two following years did so presumably knowing they would have to be canceled.

The impetus to amend the law is particularly strong among Republicans, who have voted dozens of times to repeal, defund or dismantle a program they voted against unanimously.

Unlike other GOP proposals, Upton's bill could conceivably add to the overall number of individuals gaining coverage. In political terms, it allows lawmakers to recite Obama's pledge delivered before the American Medical Association in 2009. "If you like your doctor, you will be able to keep your doctor, period," he said. "If you like your health-care plan, you'll be able to keep your health-care plan, period. No one will take it away, no matter what."