And, they warn, the TSA could lay off thousands of baggage screeners, which could force the agency to abandon full-body screening for hundreds of thousands of passengers at airports each day. (Read more: Major Airports to Remove Invasive X-Ray Body Scanners)
But because lawmakers are expected to continue negotiations in January if they can't reach agreement, government officials say there should be no immediate changes at FAA or TSA.
John Porcari, deputy secretary of transportation, explained in a memo to staffers this month that any cuts could be spread over the fiscal year until Sept. 30. He contrasted that with an immediate government shutdown, when lawmakers can't agree to spending bills.
"For these reasons, I do not expect our day-to-day operations to change dramatically on, or immediately after, Jan. 2," Porcari said. "This means that we will not be executing any immediate personnel actions, such as furloughs, on that date."
David Castelveter, a spokesman at TSA, said that "if a budget agreement is not reached, front-line screening operations would continue uninterrupted."
The airline industry group Airlines for America also isn't expecting any changes that would affect fliers.
"We are confident the FAA will ensure that air travel remains as safe as it is today, and customers should continue to book with confidence as we are not anticipating disruptions to the schedule," says Victoria Day, a spokeswoman for the group.
If Congress can't reach a compromise in the next few weeks, the automatic cuts called "sequestration" would be devastating for the agencies and some travelers for the rest of the year.
The FAA would lose more than $1 billion of its nearly $16 billion budget, according to the White House Office of Management and Budget.
Michael Huerta, FAA's acting chief, warned in October that "we could face some very drastic cuts in services" and that "these cuts would impact air-traffic control services."
"We will always, however, maintain the highest levels of safety," Huerta said.
The National Air Traffic Controllers Association released a report earlier this month that warned of furloughing 2,000 to 2,200 controllers, which "would inevitably lead to a reduction in services, reduced capacity and fewer flights."
"We urge Congress to act to prevent the sequester before it's too late," said Paul Rinaldi, the association's president.
Scott Lilly, a longtime Democratic House Appropriations Committee staffer who is now a fellow at the Center for American Progress think tank, expects those cuts to close airports.
The 29 largest hubs, such as in New York, Chicago or Atlanta, handle 70 percent of the country's 730 million annual passengers. Another 70 large airports, such as Houston's Hobby, Pittsburgh or New Orleans, handle 25 percent of the passengers. But Lilly said that leaves 340 airports handing 5 percent of passengers.
FAA had 15,236 controllers last year, so Lilly projected that more than 2,000 faced furloughs. By "educated guess," Lilly made a list in August of 106 smaller airports facing closure, topped by Savannah's Hilton Head airport in Georgia; Long Island, N.Y.; Orlando's Sanford airport in Florida; Palm Springs, Calif., and Pensacola, Fla.
"Such reckless slashing of vital services will not only fail to diminish the deficit, but will also help strangle a struggling economy," Lilly says.
Rep. Norm Dicks of Washington, the top Democrat on the House Appropriations Committee, warned separately in 2011 that the FAA cuts could close 246 air-traffic control towers.
Former Transportation secretary Norm Mineta says if the automatic cuts aren't stopped, "It will be by far the most devastating budget cut to the FAA in its 54 years."
At airports that remain open, TSA would lose more than $640 million from its $8 billion budget, according to the Office of Management and Budget. The cuts include $429 million for aviation security and $79 million for air marshals, who fly undercover to thwart hijackings.
The cuts could force TSA to eliminate 9,000 screeners and Customs and Border Protection to drop 1,600 inspection officers, according to Dicks, the lawmaker.
That would reduce staffing for full-body scanners, which are aimed at non-metallic explosives such as the attempted underwear bomber on Christmas 2009, and leave 350,000 passengers per day screened only with metal-detectors, according to Dicks.
Stephen Mullin, vice president of Econsult Corp., produced a report outlining the dangers of cuts for the advocacy group Aerospace Industries Association. He said the closer officials look, "the more destructive it turns out to be."