By Mark Felsenthal and Susan Cornwell

WASHINGTON (Reuters) - In the most significant legislative rebuke to President Barack Obama's healthcare overhaul, 39 members of his Democratic Party voted for a Republican bill in the House of Representatives on Friday aimed at undermining his signature domestic policy.

The measure, which would allow insurance companies to renew and sell inexpensive, limited-coverage policies that have been canceled because they don't meet the standards of the new healthcare law that took effect on October 1, passed 261-157.

The 39 Democrats who supported the bill - nearly one-fifth of the party's caucus - reflected the alarm that spread within Obama's party this week over the political damage from the botched rollout of the Affordable Care Act, also known as Obamacare.

Republicans have vowed to make Democratic support for the troubled law the top issue in the 2014 elections. Twenty-nine of the 39 Democrats who voted for the Republican bill are running for re-election in competitive races, according to rankings by the nonpartisan Cook Political Report.

Obama's approval ratings have plunged during the past six weeks, as the rollout of the healthcare program that is his top domestic achievement has been beset by technical glitches with the federal online insurance website designed to allow consumers to shop for policies.

In recent days, HealthCare.gov's problems have been overshadowed by reports that insurance companies were canceling the policies of millions of Americans whose policies did not meet the new law's requirements that policies cover emergency treatment, hospital stays and prescription drugs, among other things.

For years, Obama had promised that Americans would be able to keep their policies if they liked them.

But the wave of cancellations has fueled the biggest political crisis of Obama's presidency and led to an extraordinary scene at the White House on Thursday, as a contrite Obama took the blame for the healthcare program's dismal start.

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He said he believed that he had to win back the confidence of the American people, and offered an administrative "fix" that would allow some people to retain their non-conforming insurance policies for at least a year.

Obama's plan dismayed some of his supporters who say that the cheap, limited-coverage plans that the new law aims to phase out often give consumers a false sense of having meaningful health coverage.

It also created concern in the insurance industry - which for years had planned the health insurance exchanges created by Obamacare - and among state insurance commissioners.

Industry advocates warned that Obama effectively was tinkering with the delicate and complex funding behind the healthcare law, and that premiums could begin soaring in 2015 if millions of consumers who were projected to be in Obamacare's health exchanges continued to hold limited-coverage policies instead.

Obama met with health insurance chief executives at the White House on Friday to discuss his proposal's potential impact on the insurance market.

"What we're going to be doing is brainstorming on how do we make sure that everybody understands what their options are," Obama told reporters in a brief photo opportunity as the meeting began. "We're going to be soliciting ideas from them."

'FRUSTRATED AND ANGERED'

Friday's bill, introduced by Republican Representative Fred Upton of Michigan, represented the latest in a series of legislative attacks on the healthcare law by the chamber, which has held more than 40 votes to limit or curtail Obamacare.

In touting his bill, Upton said that Obama "personally promised that if people liked their current health care plan, they could keep it ‘no matter what.' But cancellation notices are now arriving in millions of mailboxes across the country. It's cancellation today, sticker shock tomorrow."

It is unlikely to pass the Democrat-controlled Senate, and the White House has said Obama would veto the legislation if it reached his desk.

The House bill would allow people whose low-cost coverage was canceled to keep those policies, and also would allow insurers to continue selling policies that do not cover basic services and offer little financial help for catastrophic health events.

Critics said the House bill would undermine Obamacare's attempt to improve the healthcare system.

House Democratic opponents cast the vote as another Republican effort to sabotage the healthcare law.

Republicans "are perfectly satisfied with 40 million Americans having no health insurance at all," said Representative James McGovern, a Massachusetts Democrat. "If you want to go back to a system where the insurance companies can turn people away because they are sick, by all means vote for this bill."

But Representative Ron Barber, a Democrat from Arizona, summarized why he and 38 other Democrats voted for the Republican bill.

"I am frustrated and angered by the continuing problems with the healthcare website and I know Southern Arizonans are frustrated and angry, too," Barber said.

"Today I voted to give people the option to keep their current plan until these and other issues are resolved. That's only fair."

House Democrats were blocked in an effort to offer a scaled-down version of Upton's bill.

(Additional reporting by Roberta Rampton and Caren Bohan; Editing by Doina Chiacu, Ross Colvin and Grant McCool)