The White House scrambled Wednesday to find solutions for the glaring failures in Obamacare as rebellious congressional Democrats pressured the administration over their increasing political predicament.

In a closed-door meeting at the Capitol, House Democrats blasted administration officials over their handling of the Obamacare rollout, and the White House’s failure to address Mr. Obama’s broken promise to Americans that they could keep their health insurance plans.

Top Senate Democrats, meanwhile, were giving more support to a legislative proposal that would allow people to keep their insurance plans. The White House said the proposal from Sen. Mary L. Landrieu, Louisiana Democrat, has more merit than a House Republican plan scheduled for a vote Friday.

Presidential aides wouldn’t commit to a specific fix.

White House press secretary Jay Carney said the president is trying to reassure congressional Democrats that he will decide on a solution “sooner rather than later.”

“The frustration that Democrats who strongly support the Affordable Care Act and who strongly believe that it is the right thing to do … [feel] is similar to the frustration the president feels,” Mr. Carney said. “Nobody is satisfied.”

The reasons for the Democrats’ rising anger are clear. With website glitches and millions of constituents receiving insurance cancellation notices, lawmakers who supported the president’s health care reform plan are feeling more vulnerable about their re-election prospects next year, and many who fought for Obamacare are worried that its promise is being threatened by incompetence.

A Quinnipiac University poll released Wednesday showed that congressional Republicans have erased a 9-point deficit in six weeks in a generic congressional ballot question, and are running even with Democrats. One of the main developments in the past six weeks was the rollout of Obamacare on Oct. 1.

Some Democrats say they were emboldened by former President Bill Clinton’s call Tuesday for Mr. Obama to make good on his “you can keep-your plan” promise even if it required legislative changes to the health care law.

Among the lawmakers who challenged administration officials in the private meeting, Democrats said, were Rep. Michael F. Doyle, Pennsylvania Democrat, and Rep. Anna G. Eshoo, a close ally of Minority Leader Nancy Pelosi, a fellow California Democrat. Administration officials taking the brunt of criticism were David Simas, deputy senior adviser to the president, and Mike Hash, director of the Health and Human Services Department’s office of health care reform.

The most urgent political challenge for House Democrats is scheduled for Friday, when they will have to vote on a plan by Rep. Fred Upton, Michigan Republican, that allows people to keep health care policies they like. Several lawmakers warned the administration officials that the White House must offer them a way out of the predicament before that vote.

Mr. Carney said the Upton bill isn’t acceptable because it would “allow insurers to sell new plans that were substandard, that did not meet the minimum benefit standard of the Affordable Care Act, and thereby potentially undermine … the central promise of the Affordable Care Act.”

Senate Democrats are scheduled to meet Thursday at the White House to urge the administration to come up with a solution.

Asked about the Quinnipiac poll’s findings that a majority of Americans for the first time find Mr. Obama untrustworthy, Mr. Carney said Washington as a whole is suffering from the fallout of the government shutdown and other failures.

“There is no question that the dysfunction in Washington that the American people have seen is taking its toll on everyone,” Mr. Carney said. “And while the president’s ratings are low for him, they’re sky high in comparison with Congress, and in particular Republicans in Congress. That’s not satisfactory to us, only because it reflects a feeling among the American people that this place is not working for them.”

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