President Obama explained how Americans who wish to keep their health plans can work to do so under his signature health-care law during a speech Friday. (The Washington Post)

The House approved a plan Friday permitting health insurance companies to continue selling policies that do not comply with the health-care law, a proposal that would allow more Americans to keep their current health plans while significantly weakening part of the Affordable Care Act.

Thirty-nine Democrats joined with the Republican majority in support of the “Keep Your Health Plan Act,” a proposal by Rep. Fred Upton (R-Mich.) that would allow insurance companies to keep selling health policies that do not reflect the Affordable Care Act’s consumer protections.

Four Republicans voted no on the bill. The 39 Democratic votes in favor represent the largest defection by far on a major or closely-watched piece of legislation this year, signaling the political difficulty that dozens of congressional Democrats face in reelection contests next year.

The proposal goes further than the administrative fix announced by President Obama Thursday, which would only allow insurers and state insurance commissioners to extend those policies through most of 2014. It faces an uphill climb in the Senate and Obama has said he would veto the bill.

But both efforts, as well as another crafted by Democrats in the Senate, are aimed at addressing the same issue: The political backlash over letters received by millions of Americans whose private health insurance policies are being canceled because of the health-care law.

The law has more headaches than just "In Play" asks some of The Washington Post's top political reporters to explain. (The Washington Post)

Republicans have seized on the letters, as well as promises by President Obama that “if you like your health plan, you can keep it,” as evidence that the health-care law is flawed and that the president has not been honest about its downsides.

“We knew this was a promise [Obama] could not keep, and now it is a promise he has broken,” House Majority Leader Eric Cantor (R-Va.) said in floor remarks.

But the remarkable support from Democrats underscored the widespread political ramifications of Obama’s broken promise.

The bill’s co-sponsors included more than 80 Republicans and three swing-district Democrats facing tough reelection contests next year: Reps. John Barrow (Ga.), Mike McIntyre (N.C.) and Patrick Murphy (Fla.).

Nervous about other potential defections, Democratic leaders dispatched several senior aides in the hours before the vote, and were seen and heard at one point talking about the vote in the hallways outside the House Chamber with Reps. Brad Schneider (D-Ill.) and Dan Maffiei (D-N.Y.), two freshmen who won tight races last year. Both ended up voted in favor of the legislation.

In another sign of the anger and frustration exhibited among Democrats this week, even Rep. Matt Cartwright (D-Pa.), a passionate defender of the new law, suggested Friday that the Obama administration waited too long to address administrative fixes to the law and put too many Democrats at political risk.

“[The White House] knew very well that they had to give us something different to support because simply stone-walling about the president’s promise and why it wasn’t kept was not going to be an option,” he said.

But like others in his party, he concluded that Obama’s fix “has given us something else to get behind. It’s not perfect, but it’s something, and more than anything it’s an acknowledgment that a promise was made and we like to honor our promises.”

Most Democrats believe that the Upton bill fundamentally guts the health law. Among its provisions is a rule that insurance plans starting next year must cover a set of 10 so-called “essential” health benefits, such as maternity care and mental health services. The House bill would allow insurers to continue to sell plans that do not meet those basic standards.

In the past 24 hours, they rallied behind Obama’s plan, which only lets people renew current plans through October of next year and requires insurers to explain ways in which the old plans do not meet the law’s stricter requirements.

“This bill is not a bill to let people keep their health insurance plans. The president took care of that issue yesterday,” Rep. Henry Waxman (D-Calif.) said in floor remarks Friday. “What this bill is, is another vote to repeal the Affordable Care Act.”

A majority of Democrats also supported a House bill that mirrors a measure introduced by Sen. Mary Landrieu (D-La.), one of several moderate Democrats facing difficult reelection contests next year. But the bill failed to advance to final passage.

Jeff Simon contributed to this report