The White House is trying to stave off a Democratic mutiny over its new health care law and on Thursday will hold a second day of emergency meetings with party lawmakers divided over how to respond to Obamacare's troubled rollout.

Sen. Mark Udall, D-Colo., is the latest Democrat to introduce legislation that would change the law that led to the cancellation of 5 million insurance policies despite the administration's repeated promise that no one would lose existing health coverage.

Udall's bill would let people keep their current plans through 2015.

"I have repeatedly said that the Affordable Care Act isn't perfect, and it will need to be improved as it is implemented," said Udall, who is up for re-election next year. "This common-sense bill ensures the health reform law allows Coloradans to maintain insurance coverage."

Senate Majority Leader Harry Reid, D-Nev., won't commit to taking up any of the fixes fellow Democrats are offering. He said Senate Democrats would meet Thursday with administration officials in hopes of quelling a growing panic over the health care law's problems.

White House officials on Wednesday talked to angry House Democrats who are up for re-election next year.

The glitch-plagued website has made it difficult for people to sign up for new health care plans -- just 106,185 were able to do so last month, administration officials announced Wednesday.

Many of those who did sign up discovered they'd be paying higher premiums and deductibles than they had with their existing plans.

Millions of Americans have received cancellation notices from their insurers because the plans they had did not meet the new law's minimum benefit requirements, which range from free mammograms to maternity care to pediatric dental coverage.

Like Udall, other vulnerable Senate Democrats have reacted to the disastrous rollout by crafting legislation that would allow many people to keep their cancelled plans.

The leading proposal, authored by Sen. Mary Landrieu, D-La., would allow people to temporarily keep health insurance plans issued before Obamacare became law in March of 2010.

Sens. Kay Hagan, D-N.C., and Mark Pryor, D-Ark., who like Landrieu face re-election fights next year in Republican-leaning states, signed on to the bill. Three other Democrats — Joe Manchin, of West Virginia; Dianne Feinstein, of California; and Jeff Merkley, of Oregon — also back the measure.

But Democratic leaders and the White House are resisting any measure that would allow people to keep insurance that doesn't meet the Obamacare standards. That kind of change could threaten the entire health care law, which hinges on millions of healthy people joining new health care exchanges, they said.

The Republican-run House will vote Friday on its own legislation to allow existing policies to continue. The bill, sponsored by House Energy and Commerce Committee Chairman Fred Upton, R-Mich., is expected to pass with significant Democratic support if Obama doesn't provide an acceptable solution by then.

White House press secretary Jay Carney said Obama would find a way "sooner rather than later" to help those whose policies were cancelled.

Carney hinted that the White House could get behind Landrieu's bill, but said the administration may also devise its own plan to help people pay for the new, more expensive plans.

Mike Tanner, a health care policy scholar at the libertarian Cato Institute, said Landrieu's plan would do the least damage to the law because it would allow people to hang on to their old policies for just a year while blocking anyone else from buying insurance that doesn't meet Obamacare standards.

But Landrieu's bill would provide only a temporary fix for the individual policy holders who can't afford the new plans, and it would mean millions of people would not join the exchanges in the first year, when critical funding levels must be met to pay for the sick and the poor who get free and subsidized care.

"It would upset the whole law," he said of Landrieu's bill. "What you have is a house of cards. It will take a real magician to be able to start pulling these cards out and not have the whole thing come crashing down."