Flight delays piled up all across the country Monday as thousands of air traffic controllers were forced to take an unpaid day off because of federal budget cuts, providing the most visible impact yet of Congress and the White House’s failure to agree on a long-term deficit-reduction plan.

The Federal Aviation Administration kept planes on the ground because there weren’t enough controllers to monitor busy air corridors. Cascading delays at some of the nation’s busiest airports held up many flights into New York, Baltimore and Washington by more than two hours.

In the morning, the delays were so bad that passengers on several Washington-New York shuttle flights could have reached their destination faster by taking the train.

Nearly a third of flights at New York’s LaGuardia airport scheduled to take off before 3 p.m. were delayed 15 minutes or more, according to flight-tracking service FlightAware. Last Monday, just 6 percent of LaGuardia’s flights were delayed.

The situation was similar at Washington’s Reagan National Airport, in Newark, N.J., and in Philadelphia with roughly 20 percent of flights delayed.

Monday is typically one of the busiest days at airports with many high-paying business travelers departing for a week on the road. The FAA’s controller cuts — a 10 percent reduction of its staff — went into effect Sunday. The full force was not felt until Monday morning.

Travel writer Tim Leffel had just boarded a US Airways plane from Charlotte, N.C., to Tampa, when the flight crew had an announcement.

“They said: ‘The weather’s fine, but there aren’t enough air traffic controllers,’ ” Leffel said. Passengers were asked to head back into the terminal. “People were just kind of rolling their eyes.”

His flight landed one hour and 13 minutes late.

One thing working in fliers’ favor Monday was relatively good weather at most of the country’s major airports. A few wind gusts in New York, snow in Denver and thunderstorms in Miami added to some delays, but generally there were clear skies and no major storms.

However, the shortage of controllers could persist for months, raising the risk of a turbulent summer travel season. And it could exacerbate weather problems, especially spring and summer thunderstorms.

There’s no way for passengers to tell in advance which airport or flights will experience delays.

FAA officials have said they have no choice but to furlough all 47,000 agency employees — including nearly 15,000 controllers — because the agency’s budget is dominated by salaries. Each employee will lose one day of work every other week. The FAA has said that planes will have to take off and land less frequently, so as not to overload the remaining controllers on duty.

Critics have said the FAA could reduce its budget in other spots that wouldn’t delay travelers.

“There’s a lot finger-pointing going on, but the simple truth is that it is Congress’s job to fix this,” said Rep. Rick Larsen, a Washington Democrat and member of the House aviation panel. “Flight delays are just the latest example of how the sequester is damaging the economy and hurting families across the country.”

Some travel groups have warned that the disruptions could hurt the economy.

“If these disruptions unfold as predicted, business travelers will stay home, severely impacting not only the travel industry but the economy overall,” the Global Business Travel Association warned the head of the FAA, Michael P. Huerta, in a letter Friday.