The Associated Press / People wait in line Sunday to check in to American Airlines flights at Chicago O’Hare International Airport in Chicago, Ill.

WASHINGTON — U.S. airlines canceled more than 2,700 flights on Sunday as Transportation Secretary Sean Duffy warned that air traffic across the nation would “slow to a trickle” if the federal government shutdown lingered into the busy Thanksgiving travel holiday season.

The slowdown at 40 of the nation’s busiest airports began to cause more widespread disruptions in its third day. The FAA last week ordered flight cuts at the nation’s busiest airports as some air traffic controllers, who have gone unpaid for nearly a month, have stopped showing up for work.

In addition, nearly 10,000 flight delays were reported on Sunday alone, according to FlightAware, a website that tracks air travel disruptions. More than 1,000 flights were canceled Friday, and more than 1,500 on Saturday.

The FAA reductions started Friday at 4% and were set to increase to 10% by Nov. 14. They are in effect from 6 a.m. to 10 p.m. local time and will impact all commercial airlines.

Hartsfield-Jackson International Airport in Atlanta stood to have the most cancellations Sunday, followed by Chicago O’Hare International, where wintry weather threatened. In Georgia, weather could also be a factor, with the National Weather Service office in Atlanta warning of widespread freezing conditions through Tuesday.

Traveler Kyra March finally arrived at Hartsfield-Jackson on Sunday after a series of postponements the day before.

“I was coming from Tampa and that flight got delayed, delayed, delayed. Then it was canceled and then rebooked. And so I had to stay at a hotel and then came back this morning,” she said.

The FAA said staffing shortages at Newark and LaGuardia Airport in New York were leading to average departure delays of about 75 minutes.

Detroit Metropolitan Wayne County Airport in Michigan was mostly empty Sunday morning, with minimal wait times at security checkpoints as delays and cancellations filled the departures and arrivals boards.

Earlier Sunday, Duffy warned that U.S. air traffic could decline significantly if the shutdown persisted. He said additional flight cuts — perhaps up to 20% — might be needed, particularly if controllers receive no pay for a second straight pay period.

“More controllers aren’t coming to work day by day, the further they go without a paycheck,” Duffy told “Fox News Sunday.”

And he prepared Americans for what they could face during the busy Thanksgiving holiday.

“As I look two weeks out, as we get closer to Thanksgiving travel, I think what’s going to happen is you’re going to have air travel slow to a trickle as everyone wants to travel to see their families,” Duffy said.

With “very few” controllers working, “you’ll have a few flights taking off and landing” and thousands of cancellations, he said.