Approval came without dissent, and long after many senators had left the Capitol for a weeklong vacation.
A House vote is expected as early as Friday.
The Federal Aviation Administration is being forced to trim $637 million for the rest of the fiscal year, but under the new measure, the FAA would gain authority to transfer up to $253 million from accounts that are flush into other programs, to "prevent reduced operations and staffing" through the Sept. 30 end of the fiscal year.
Officials said that would likely be enough to restore full staffing for the furloughed controllers, as well as prevent the closure of small airport towers.
Last month, the federal government announced that Sugar Land Regional Airport and Lone Star Regional airport are among the 149 airports that would lose their air traffic controller towers because of budget cuts.
The closures would not have forced the shutdown of any of those airports, but pilots would have been left to coordinate takeoffs and landings among themselves over a shared radio frequency with no help from ground controllers under procedures that all pilots are trained to carry out.
The plan immediately raised concerns since a preliminary list of facilities was released a month ago. Those worries include the impact on safety and the potential financial effect on communities that rely on airports as key economic engines for attracting businesses and tourists.
Sugar Land city leaders were not only worried about the impact on safety, but the economic fallout. Sugar Land has grown to more than 80,000 people, and dozens of Fortune 500 companies use the airport, where clearing customs can go more quickly.
"Closing that tower is a really bad option," Sugar Land Spokesperson Doug Adolph told Eyewitness News last month. "This airport is not a highway to nowhere. It's not somebody's special port project. It's an important part of the economy."
The Senate acted as the FAA said there had been at least 863 flights delayed on Wednesday "attributable to staffing reductions resulting from the furlough."
There was no immediate reaction at the White House, although administration officials participated in the negotiations that led to the deal and evidently registered no objections.
Sen. Susan Collins, R-Maine, a key participant in the talks, said the legislation would "prevent what otherwise would have been intolerable delays in the air travel system, inconveniencing travelers and hurting the economy."
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.
In an interview Wednesday, Robert Isom, chief operations officer of US Airways, likened the furloughs to a "wildcat regulatory action."
He added, "In the airline business, you try to eliminate uncertainty. Some factors you can't control, like weather. It (the FAA issue) is worse than the weather."
In a shift, first the White House and then senior Democratic lawmakers have signaled a willingness in the past two days to support legislation that alleviates the budget crunch at the FAA, while leaving the balance of the $85 billion to remain in effect.
Obama favors a comprehensive agreement that replaces the entire $85 billion in across-the-board cuts as part of a broader deficit-reduction deal that includes higher taxes and spending cuts.
One Senate Democrat, Sen. Patty Murray of Washington, noted that without the type of comprehensive deficit deal that Obama favors, a bill that eases the spending crunch at the FAA would inevitably be followed by other single-issue measures. She listed funding at the National Institutes of Health as one example, and cuts that cause furloughs of civilians who work at military hospitals as a second.
At the same time, Democratic aides said resolve had crumbled under the weight of widespread delays for the traveling public and pressure from the airlines.
Sen. John Thune, R-S.D., involved in the discussions, said the issue was big enough so "most people want to find a solution as long as it doesn't spend any more money."
Officials estimate it would cost slightly more than $200 million to restore air traffic controllers to full staffing, and another $50 million to keep open smaller air traffic towers around the country that the FAA has proposed closing.
Across the Capitol, the chairman of the House Transportation Committee, Rep. Bill Shuster, R-Pa., said, "We're willing to look at what the Senate's going to propose."
He said he believes the FAA has the authority it needs under existing law to shift funds and end the furloughs of air traffic controllers, and any legislation should be "very, very limited" and direct the agency to use the flexibility it already has.
In a reflection of the political undercurrents, another House Republican, Rep. James Lankford of Oklahoma, said FAA employees "are being used as pawns by this (Obama) administration to be able to implement the maximum amount of pain on the American people when it does not have to be this way."
The White House and congressional Democrats vociferously dispute such claims.
The Associated Press contributed to this report
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