NEW YORK (AP) -- The pain Americans are facing at airports across the country is expected to get worse this week if Congress is unable to reach a deal to reopen the federal government.

U.S. airlines canceled more than 1,500 flights Saturday and more than 2,900 Sunday to comply with an FAA order to reduce traffic as some air traffic controllers, who have gone unpaid for nearly a month, have stopped showing up for work.

As of early Monday, airlines had already canceled nearly 1,600 flights for Monday and nearly 1,000 for Tuesday.

The Senate took a first step toward ending the shutdown Sunday, but final passage could still be several days away and experts have said it will take time for flights to go back to normal even after the government reopens.

Many airports are facing significant delays for flights that haven't been canceled as well, with airports in Newark, Orlando, Chicago and Detroit all facing departure delays of more than an hour and increasing, according to FlightAware.

This is the second pay period that air traffic controllers have not received any pay for their work. The head of the air traffic controllers union, Nick Daniels, will hold a press conference Monday morning to address the impact the shutdown is having on them.

The delays and cancellations are likely to get worse as airlines are increasingly unable to reposition planes, pilots and flight attendants due to the air traffic controller shortage.

The FAA implemented a 4% mandatory reduction in flights this weekend to manage staffing. That will increase to 6% on Tuesday and 10% reduction by this upcoming weekend. Transportation Secretary Sean Duffy said on "Fox News Sunday" that additional flight cuts of up to 20% might be needed.

"More controllers aren't coming to work day by day, the further they go without a paycheck," Duffy said.

The government has been short of air traffic controllers for years, and multiple presidential administrations have tried to persuade retirement-age controllers to remain on the job. Duffy said the shutdown has exacerbated the problem, leading some air traffic controllers to speed up their retirements.

While 4% may sound modest, much of that reduction is happening at 40 of the nation's busiest and most congested airports. The FAA says the flight reduction is necessary to keep travelers safe as many of the remaining controllers have been putting in long hours and mandatory overtime while the government remains unfunded.

If not addressed soon, the situation could get even worse as the U.S. heads into the busy holiday travel season. Duffy said that air travel may "be reduced to a trickle" by the week of Thanksgiving.

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Associated Press writers Stephen Groves and Kevin Freking contributed to this report from Washington. Associated Press writer Rio Yamat contributed from Las Vegas.