Some groups have filed suit to stop the furloughs of air traffic controllers. The FAA must cut hundreds of millions under federal budget sequestration. - 

Monday is the first big travel day at American airports since the FAA began furloughing air traffic controllers over the weekend. The agency needs to cut nearly $640 million from its budget in response to the federally mandated sequestration. That could lead to delays that the industry is not happy about.

"Air traffic controllers should not be furloughed -- period," says Lee Moak, who heads the Air Line Pilots Association. His group has joined Airlines for America in a lawsuit that would stop the FAA from cutting back what they call essential airport personnel.

"These furloughs will impact airports coast-to-coast every single day," Moak says.

The FAA would not comment for this story. But the agency said last week that it will furlough 47,000 employees through September. Worst case, the FAA predicts travelers in Atlanta could see flight delays of more than three hours; Chicago O'Hare, two hours plus.

Charlie Leocha directs the Consumer Travel Alliance. He says right now all customers can do is show up at the airport and hope for a smooth trip.

"That's basically the only recourse we have," Leocha says. "So far, airlines have not agreed to allow passengers to rebook flights or change their flights for no cost."

A spokesman for New York area airports says extra customer service reps will be deployed this week, and information about delays will be posted online.