WASHINGTON - Furloughed air traffic controllers will soon be heading back to work, ending a week of coast-to-coast flight delays that left thousands of travelers frustrated and furious.

Unable to ignore the travelers' anger, Congress overwhelmingly approved legislation Friday to allow the Federal Aviation Administration to withdraw the furloughs. The vote underscored a shift by Democrats who had insisted on erasing all of this year's $85 billion in across-the-board budget cuts, not just the most publicly painful ones, for fear of losing leverage to restore money for Head Start and other programs with less lobbying clout and popular support.

With President Barack Obama's promised signature, the measure will erase one of the most stinging and publicly visible consequences of the budget-wide cuts known as the sequester.

Friday's House approval was 361-41 and followed the previous evening's passage by the Senate, which didn't even bother with a roll call. Lawmakers then streamed toward the exits — and airports — for a weeklong spring recess.

White House spokesman Jay Carney said Obama would sign the bill, but Carney complained that the measure left the rest of the sequester intact.

"This is a Band-Aid solution. It does not solve the bigger problem," he said. Using the same Band-Aid comparison, Rep. Rick Larsen, D-Wash., said that "the sequester needs triple bypass surgery."

The FAA and Transportation Department did not respond to repeated questions about when the controllers' furloughs would end. Sen. Susan Collins, R-Maine, who helped craft the measure, was told by Transportation Secretary Ray LaHood Friday that the agency is "doing everything they can to get things back on track as quickly as possible," said Collins spokesman Kevin Kelley.

In the week since the furloughs began, news accounts have prominently featured nightmarish tales of delayed flights and stranded air passengers. Republicans have used the situation to accuse the Obama administration of purposely forcing the controllers to take unpaid days off to dial up public pressure on Congress to roll back the sequester.

"The president has an obligation to implement these cuts in a way that respects the American people, rather than using them for political leverage," House Speaker John Boehner, R-Ohio, said in a written statement.

"Unfortunately for this administration, the term `sequester' has become synonymous with fear," Rep. Richard Hudson, R-N.C., said during the debate.

Halting the furloughs was the latest example of lawmakers easing parts of the sequester that became too painful.

They previously used a separate, wide-ranging spending bill to provide more money for meat and poultry inspectors. Attorney General Eric Holder cited extra funds in that same bill as the reason the Justice Department would be able to avoid furloughs. Transportation Security Administration employees also have gotten relief.

The Obama administration and congressional Democrats — backed by many fiscal experts — say the sequester law gives agencies little maneuverability, requiring them to spread cuts evenly among most budget accounts. The Federal Aviation Administration was achieving about a third of its required $637 million in cuts by furloughing nearly all its workers — including the 15,000 air traffic controllers — one day every two weeks.

Obama and his Democratic allies want to roll back the entire sequester, with the White House proposing a substitute mix of spending cuts and tax increases that Republicans have rejected. The GOP has proposed replacing the across-the-board spending cuts with others, many of them aimed at programs Democrats defend.

That has left many Democrats reluctant to ease across-the-board cuts for individual programs that cause a public outcry because they worry that would relieve pressure on Republicans to undo the entire sequester.

"While there is a little bit of leverage and pressure, let's broaden it to the sequester as a whole," Rep. Tim Walz, D-Minn., told reporters before voting against the bill.

Said House Minority Leader Nancy Pelosi, D-Calif.: "How can we sit there and say, `Four million Meals on Wheels for seniors gone? But that's not important. Over 70,000 children off Head Start. But that's not important.' What is important is for Republicans to hold a hard line" on budget cuts.

Even so, the complaints about flying delays became too intense, and in the end only 29 Democrats and 12 Republicans voted against the measure Friday in the House. The FAA said there had been at least 863 flights delayed on Wednesday attributed to the furloughs, with hundreds of others daily since the furloughs began last Sunday.