(Elaine Thompson/AP)

Sequestration became a reality to the broad public in airports across the country this week, and on Friday both Congress and the White House caved in to pressure from tens of thousands of airline passengers angered by flight delays.

The lawmakers and the Obama administration, creators of the across-the-board funding cuts, found a path around their own creation, approving legislation to end the daily furloughs of 1,500 air traffic controllers that caused long delays at several major airports.

The House voted 361 to 41 Friday in favor of a bill that had won unanimous support in the Senate, and White House press secretary Jay Carney said President Obama would sign it.

With Congress headed home for a week, the question becomes whether lawmakers will return emboldened to keep tinkering with sequestration, giving more federal agencies the flexibility to make required budget cuts in ways that do not call for furloughs or unpopular service cuts.

The White House had pushed for Congress to eliminate sequestration, but its hand was forced Friday. Now, it faces the risk that if Congress continues to mandate small spending changes that reduce the high-profile and painful consequences of the cuts, the entire sequestration process will become more palatable to the public.

House Transportation Committee Chairman Bill Shuster (R-Pa.) hinted at that possibility after Friday’s vote.

“This legislation ensures beyond a shadow of a doubt that the agency now has more than enough capacity to end air traffic controller furloughs, stop the pain for the traveling public and protect the economy,” Shuster said, “without giving the FAA any additional funding.”

The Federal Aviation Administration furloughs may have been the most visible effect of the $85 billion in spending cuts that kicked in across the government on March 1 after a gridlocked Congress failed to reach agreement on a broad plan to reduce the federal deficit. The cuts had been designed to be so painful and indiscriminate — mindless, even — that even a partisan Congress would not allow them to happen.

Republicans see the changes in FAA spending ordered by the new legislation as a model for future adjustments to the cuts. They are pushing legislation to give the administration more flexibility to administer the sequester while leaving in place the overall spending reductions the law requires.

But the White House, which seemed taken by surprise by the bill’s swift passage, resumed the push to end sequestration.

“The problem is that this is just a Band-Aid solution,” Carney said. “Congress should do the responsible thing and stop dealing with these issues from crisis to crisis, and simply engage in a discussion about how we can eliminate the sequester entirely through balanced deficit reduction.”

The furlough of 1,500 air traffic controllers each day to achieve $200 million in savings from the FAA’s budget became a test of wills between Congress and the administration.

Republicans said the president abruptly announced the details of the furlough plan last week to create a high-profile, television-friendly display of its impact. They contended that the FAA had other options for mandated cuts that totaled $637 million.

“The administration has played shameful politics,” Rep. Tom Latham (R-Iowa) said during the House debate.

The FAA denied it had that flexibility. It was unable to say after the House voted when the furloughed controllers might return to their jobs.

Friday was one of the busiest travel days of the week, and all three of New York’s major airports were reporting furlough-related delays. Problems at those airports often ripple through the system.

Federal officials had predicted that the controller furloughs would result in as many as 6,700 flight delays each business day. Through Thursday, the number of flights arriving or departing behind schedule averaged about 2,800 a day, with many of them attributed to weather problems at hub airports.

The reprieve for the FAA controllers is a lesson in how, less than two months after it kicked in, a law designed to inflict pain in almost every corner of the government has quickly created winners and losers in the federal workforce.

“Instead of solving sequestration responsibly, it is easier to grant flexibility to more politically palatable programs,” said Rep. Donna F. Edwards (D-Md.), who opposed the original plan for automatic spending cuts. “We must summon the courage and compassion to deal with sequestration as a whole and help those impacted by Congress’s inability to deal with our budget responsibly.”

Friday’s vote moves the government toward a system of targeted budget cuts instead of across-the-board cuts. The result is that agencies with political clout on Capitol Hill, or whose mission is visible to ordinary Americans, have been able to eliminate or significantly reduce furloughs that just weeks ago threatened to total 22 days at some agencies this fiscal year.

“There’s no justice or evenhandedness about it whatsoever,” said Scott Lilly, a congressional budget expert and senior fellow at the Center for American Progress, a liberal think tank.

“Programs that haven’t been run well are not affected by sequestration, and ones that are totally effective are getting hammered,” Lilly said. “It’s totally irrational.”

At many agencies, the response to sequestration is still unresolved.

Hundreds of thousands of civil servants remain in limbo as they try to plan summer vacations and arrange for child care weeks before school lets out.

Almost 800,000 civilian employees at the Defense Department were told at first they would lose 22 days of pay, an assessment that changed to 14 days a few weeks ago. As of Friday, Defense Secretary Chuck Hagel was reviewing whether the number could fall further. The Justice Department announced this week that it would not have to resort to furloughs, after sending notices to employees that warned of as many as 14 unpaid days. The government’s temporary budget granted those agencies the flexibility in March to adjust furlough days.

The inequity rankles federal workers forced to deal with big hits to their paychecks while in the third year of a salary freeze.

“I think it’s unfair,” Elizabeth Lytle, an administrative program assistant for the EPA’s Chicago office, said Friday after the FAA vote in the House. “They have literally thousands of people they must protect. But guess what? There are others of us that would like to have that reprieve, too.”

To replace the sequester’s mandatory reductions, Obama wants a package of alternative spending cuts and new tax revenue achieved by scaling back tax breaks that benefit the wealthy. But Republicans have resisted, and Obama is now engaged in private dinners and conversations with lawmakers to press his case.

Friday’s debate in the House was a show of bipartisan disdain for the process of spending cuts, embroidered at every turn with partisan finger-pointing.

“Sequestration is a dumb way to do business — it cuts the good with the bad, without regard for critical federal programs or the needs of the American people,” said House Appropriations Committee Chairman Rep. Harold Rogers (R-Ky.).

“Before we start patting each other on the back for this bill, I think it’s important that we recognize that we’re not fixing the bigger problems that sequester has created,” said Rep. Rick Larsen (D-Wash.). “This lands somewhere short of a profile in courage. This is a Band-Aid, and sequestration needs a triple-bypass surgery. Congress created this problem. We need to fix it.”

Zachary A. Goldfarb and Josh Hicks contributed to this report.