Transportation Secretary Ray LaHood said thousands of people could be put out of work.
"This is no way to run the best aviation system in the world," LaHood said.
Congress has not reached an agreement on legislation to extend the FAA's operating authority, which must happen by midnight.
The main obstacle is a provision sought by House Republicans and the airline industry that would make it more difficult for airline and railroad workers to unionize. The provision was added to a long-term FAA funding bill earlier this year, but negotiations on that bill have stalled. Without long-term legislation, an extension bill is necessary to keep the agency operating.
If the FAA shuts down, LaHood said the government will lose about $200 million a week in airline ticket taxes, and several construction projects will come to a halt.
Air traffic controllers would remain on the job, and safety would be maintained.
If there is no extension, initially the largest furlough would involve nearly 1,000 workers at FAA headquarters in Washington, transportation officials said.
Passengers could see big savings.
Barring an agreement, FAA taxes will disappear from airline and ticket selling websites at midnight.
The Associated Press contributed to this story.