Reid said Tuesday that if Democrats don't succeed in passing their own bill to restore the FAA's operating authority, they will accept a House bill containing the cuts.
The agency's operating authority was allowed to expire on July 23 in a legislative standoff between the Democratic-controlled Senate and the GOP-controlled House.
As a result, the government is losing $30 million a day in airline ticket taxes.
THIS IS A BREAKING NEWS UPDATE. Check back soon for further information. AP's earlier story is below.
The congressional standoff that has partially shut down the Federal Aviation Administration has some curious math.
Lawmakers risk losing more than $1 billion in revenue from uncollected airline ticket taxes in a quarrel between Senate Democrats and House Republicans who are demanding a $16.5 million cut in rural air service subsidies.
The shutdown is less than two weeks old and already the government has lost more than $250 million in revenue because airlines' authority to collect ticket taxes has expired. The entire annual budget of the rural air services program is about $200 million.
"I'm a fiscal conservative," Sen. Kay Bailey Hutchison, R-Texas, told the Senate on Monday. "I'm trying to make the cuts that are necessary, trying to do the things that are right, but ... that just doesn't add up."
The Senate, with the federal debt crisis resolved, is expected to leave by the end of the week for its August recess. The House has already left. Unless the Senate accepts the House bill, lost revenue from uncollected airline ticket taxes could exceed $1.2 billion before lawmakers return to work a month later, senators said.
The FAA's long-term operating authority expired in 2007. Since then, Congress has been unable to agree on a long-term funding plan. The agency has continued to operate under a series of 20 short-term extensions.
The latest extension expired at midnight on July 22 after Senate Democrats rejected a temporary extension bill passed by the House that contained the subsidy cuts. Senate Republicans blocked a Democratic extension that didn't include cuts.
The lost ticket tax revenue is costing the government an estimated $200 million a week. The FAA has furloughed nearly 4,000 employees and issued stop-work orders on more than 200 construction projects.
Air traffic controllers have remained on the job. Transportation Secretary Ray LaHood has vowed that safety won't be compromised and travelers won't be inconvenienced
Democrats say the subsidies fight is actually a ploy to get them to accept a GOP labor provision in a separate, long-term FAA funding bill passed by the House. Republicans deny that's the case.
"Senate Democrats are also arguing that the House-passed extension is about a labor provision, but the fact is there is no labor provision in the extension," Rep. John Mica, R-Fla., the House Transportation and Infrastructure Committee chairman, told colleagues in a letter last week.
Three times in the last 10 days, senators' efforts to pass a bill to end the shutdown without making air service subsidy cuts have been blocked by Sen. Orrin Hatch, R-Utah. Each time, Hatch has focused his remarks on the labor provision.
"I've been asked by our leadership to make these objections," Hatch explained Monday night. "What is important here — and it's not some itty-bitty little thing — is that you have labor regulators out of control."
To end the shutdown, he said, the Senate must agree to the House's labor provision. Then, the shutdown "would be solved in a nanosecond," he said.
The labor provision would overturn a National Mediation Board rule approved last year that allows airline and railroad employees to form a union by a simple majority of those voting. Under the old rule, workers who didn't vote were treated as "no" votes.
Republicans complain that the new rule reverses 75 years of precedent to favor labor unions. Democrats and union officials say the change puts airline and railroad elections under the same democratic rules required for unionizing all other companies.
The White House warned in March that President Barack Obama would veto an FAA bill containing the labor provision.