Senate approval followed several hours of pressure-filled, closed-door negotiations, and came after most senators had departed the Capitol on the assumption that the talks had fallen short.
Officials said a small group of senators insisted on a last-ditch effort at an agreement before Congress adjourned for a vacation that could have become politically problematic if the flight delays continued.
"I want to do it right now. There are other senators you'd have to ask what the hang-up is," Sen. Mark Udall, D-Colo., said at a point when it appeared no compromise would emerge.
For the White House and Senate Democrats, the discussions on legislation relating to one relatively small slice of the $85 billion in spending cuts marked a shift in position in a long-running struggle with Republicans over budget issues. Similarly, the turn of events marked at least modest vindication of a decision by the House GOP last winter to finesse some budget struggles in order to focus public attention on the across-the-board cuts in hopes they would gain leverage over President Barack Obama.
The Professional Aviation Safety Specialists, a union that represents FAA employees, reported a number of incidents it said were due to the furloughs.
In one case, it said several flights headed for Long Island MacArthur Airport in New York were diverted on Wednesday when a piece of equipment failed. "While the policy for this equipment is immediate restoral, due to sequestration and furloughs it was changed to next-day restoral," the union said.
It added it was "learning of additional impacts nationwide, including open watches, increased restoration times, delays resulting from insufficient funding for parts and equipment, modernization delays, missed or deferred preventative maintenance, and reduced redundancy."
The airlines, too, were pressing Congress to restore the FAA to full staffing.