WASHINGTON — Brushing aside a White House veto threat, the Republican-controlled House voted by a healthy bipartisan majority Friday to weaken a core component of “Obamacare” and permit the sale of individual health coverage that falls short of requirements in the law.

In all, 39 Democrats broke ranks and supported the legislation, a total that underscored the growing importance of the issue in the weeks since millions of cancellation notices went out to consumers covered by plans deemed inadequate under government rules.

The final vote was 261-157 as lawmakers clashed over an issue likely to be at the heart of next year’s midterm elections. The measure faces an uncertain fate in the Senate, where Democrats seeking re-election in 2014 are leading a move for generally similar legislation.

“For the last six weeks the White House stood idly by ignoring the pleas of millions,” said Rep. Fred Upton, R-Mich., chairman of the House Energy and Commerce Committee and lead sponsor of the legislation.

“Our straightforward, one-page bill says, if you like your current coverage, you should be able to keep it. The president should heed his own advice and work with us, the Congress, as the founders intended, not around the legislative process.”

But Democrats said the measure was just another in a long line of attacks on the health care bill from Republicans who have voted repeatedly to repeal it.

“It would take away the core protections of that law. It creates an entire shadow market of substandard health care plans,” said Rep. Henry Waxman of California.

The vote came shortly before President Barack Obama welcomed insurance company CEOs to a White House meeting, and one day after he announced a shift toward making good on his oft-repeated promise that anyone liking his pre-Obamacare coverage would be able to keep it.

In brief opening remarks, he did not refer to the House vote, and showed no give in his commitment to the program known by his name. “Because of choice and competition, a whole lot of Americans who have always seen health insurance out of reach are going to be in a position to purchase it,” he said.

The events capped a remarkable series of politically inspired maneuvers in recent days. The president and lawmakers in both parties have sought to position themselves as allies of consumers who are receiving cancellation notices — yet have made no move to cooperate on legislation that could require those consumers’ coverage to be renewed if they wanted to keep it.

Neither Obama’s new policy nor the bill passed in the House would ensure that anyone whose policy is canceled will be able to keep it. Instead, both would permit insurance companies to sell coverage renewals if they wish — subject to approval by state insurance commissioners.

The White House meeting came as the industry and state commissioners began adjusting to the president’s one-day-old change in policy.

Under the shift, Obama said insurers should be permitted to continue to sell to existing customers individual coverage plans that would be deemed substandard under the health care law. Without the change, many existing plans would have been banned beginning next year, and the president’s announcement was an attempt to quell a public and political furor triggered by millions of cancellation notices.

The House measure went one step further. It would give insurance firms the ability to sell individual plans to new as well as existing customers, even if the coverage falls short of the law’s requirements.

Democrats sought to substitute a plan of their own that consisted largely of Obama’s new policy, but failed on a party-line vote.

Even so, the combination of the president’s announcement and his party’s alternative apparently siphoned off a large number of Democratic votes from the GOP measure.

In a veto threat Thursday night, the White House accused Republicans of seeking to “sabotage the health care law,” and said their measure would allow “insurers to continue to sell new plans that deploy practices such as not offering coverage for people with pre-existing conditions, charging women more than men, and continuing yearly caps on the amount of care that enrollees receive.” A veto would come into play only if both houses approve legislation and send it to the White House for the president’s signature.

Political calculations were evident as Obamacare produced yet more controversy.

The political arms of both parties in both houses churned out attacks all week that underscore the importance of the issue in the 2014 elections. Additionally, Obama made an unusual attempt on Thursday to shelter any Democrat who may have said when the bill was under consideration in 2010 — as he did — that anyone wanting to keep current coverage would be permitted to.

“They were entirely sincere about it,” he said of the lawmakers. “It’s not on them, it’s on us.”

In the Senate, a handful of Democrats who face tough re-election races next year, led by Sen. Mary Landrieu of Louisiana, are supporting legislation to require insurance companies to renew policies cancelled because of the law.

Under the law, plans generally are required to meet numerous conditions to qualify. Among them, they would have to accept all customers, regardless of pre-existing conditions, would be limited in additional premiums they could charge on the basis of age and could not cap lifetime benefits. They also would have to provide coverage in a wide range of areas — doctor and hospital care for adults and children, laboratory services, preventive coverage and prescription drugs among them.

The cancellation issue is only part of the woes confronting the president and his allies as they struggle to sustain the health care law.

Obama has repeatedly apologized for a dismal launch of www.healthcare.gov , which consumers in 36 states were supposed to use beginning on Oct. 1 to sign up for new coverage. The website is so riddled with problems that the administration disclosed earlier this week that fewer than 27,000 signups have been completed — a number that Republicans noted is dwarfed by the flood of cancellations issued due to the law.

Compounding the administration’s misery, the poor quality of the website has made it that much harder for consumers receiving cancellation notices to shop for alternative plans.

It is unclear what, if anything, the administration is prepared to do to alleviate the threat of a break in coverage for those consumers.

Associated Press writers Ricardo Alonso-Zaldivar, Julie Pace and Alan Fram in Washington and David Eggert in Detroit contributed to this report.