– Anxious congressional Democrats are threatening to abandon President Obama on a central element of his signature health care law, voicing increasing support for proposals that would allow Americans who are losing their health insurance coverage because of the Affordable Care Act to retain it.

The dissent comes as the White House released enrollment figures Wednesday that fell far short of expectations, and as House Republicans continued their criticism of the administration during congressional hearings examining the performance of the health care website and possible security risks of the online insurance exchanges.

In addition, a vote is scheduled Friday in the Republican-controlled House on a bill that would allow Americans to keep their existing health coverage through 2014 without penalties. The measure, drafted by Rep. Fred Upton, R-Mich., chairman of the Energy and Commerce Committee, is opposed by the White House, which argues that it would undermine the Affordable Care Act by allowing insurance companies to continue to sell health coverage that does not meet the higher standard of Obama’s health care law.

But a growing number of House Democrats, reflecting a strong political backlash to the law’s rollout, are warning that they might support the measure if the administration does not provide a strong alternative argument.

Tensions flared during a closed-door meeting Wednesday of House Democrats and White House officials, as several lawmakers upbraided the administration, saying that the president had put Democrats in a difficult political position by wrongly promising consumers that they could keep their existing health care plans. In fact, hundreds of thousands of Americans have received cancellation notices from their insurers because their health care coverage does not meet the minimum standards dictated by the new law.

“I’m frustrated in how it rolled out, and I let them know in no uncertain terms,” said Rep. Mike Doyle, D-Pa.

“The point I was making in caucus to the administration is ‘Don’t give us this techno-babble that you’re going to do some administrative fix down the road.’ There’s a bill being put on the floor on Friday.”

The overall message of the meeting, said several attendees, was that the White House and the House Democratic leadership have until Friday to come up with a satisfactory alternative, or House Democrats might be forced to support Upton’s bill, which has two Democratic co-sponsors: Reps. John Barrow of Georgia and Mike McIntyre of North Carolina, who represent more conservative districts.

“I think the Upton bill is terrible, but we need something else to vote for in order to keep our word to the American people,” Doyle added.

“We told people in those plans that they were grandfathered in, and if they wanted to stay in them, they could, and we need to honor that.”

A similar proposal, which would allow people to keep their current health insurance permanently, is also drawing support in the Senate under an effort led by Sen. Mary L. Landrieu, D-La. Landrieu said she remained committed to her bill, despite White House expressions of reluctance to embrace a legislative fix. Still, White House spokesman Jay Carney said Wednesday that the Landrieu proposal shared “a similar goal to what the president has asked his team to explore.”

Landrieu drew a distinction between her plan — which she said would maintain the key provisions of the Affordable Care Act — and those offered by Republicans that would dismantle the law, like the one introduced by Upton.

Administration officials conceded that the bungled health care rollout had produced a turbulent political situation in Washington. But they said they were confident that fixing the website, HealthCare.gov, would help Democrats in next year’s elections.

Carney said that the president’s top aides were working to come up with an administrative fix to the problem of the cancellation of health insurance plans. But he declined to say when that would be announced or whether it would come before Democrats are asked to vote Friday.

Insurance companies, deeply worried about the low enrollment in the plans they are offering on the insurance exchanges, say congressional proposals to force them to allow canceled policies to be reissued could be disastrous. Robert Zirkelbach, a spokesman for America’s Health Insurance Plans, the industry’s lobby, said insurers had “significant concerns on how it would work operationally.”