By Jennifer Liberto and Mike Ahlers@CNNMoneyApril 23, 2013: 2:43 PM ET
Air travelers headed into New York's LaGuardia Airport were facing two hour delays on Tuesday morning.
By Tuesday afternoon La Guardia's delays had improved by as much as an hour for some flights.
With fewer air traffic controllers showing up to work, the government has warned of problems at several large airports including those in the New York area, Los Angeles, Dallas-Ft. Worth and Las Vegas. The Department of Transportation warned that those airports are facing "staffing challenges" on Tuesday.
There were 1,200 delays on Monday specifically tied to fewer air traffic controllers at work, according to the transportation agency. Weather and other factors caused another 1,400 delays. On Sunday, the agency reported 400 delays due to furloughs.
By Tuesday, delays eased for the rest of the country.
The FAA is trying to deal with $600 million in forced spending cuts by September. Transportation Secretary Ray LaHood has said he had no choice but to resort to furloughs at the FAA. In a call with reporters on Tuesday, he dismissed accusations that FAA furloughs are politically motivated to make budget cuts feel worse than they are.
"Obviously people haven't been paying attention to Ray LaHood, I've been talking about (furloughs) for a few months," said LaHood, who is a Republican. "There is absolutely no politics involved in this at all. This is bad policy that Congress passed and they should fix it."
At La Guardia, a dozen employees out of 47 total, were forced to take an unpaid day off from work on Tuesday, said Doug Church, spokesman for the National Air Traffic Controllers Association.
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"Weather is not a factor in those delays," Church said.
New York's John F. Kennedy International wasn't as badly affected because just three or four employees out of 37 were on furlough on Tuesday, said Steve Abraham, a controller at JFK airport.
"Right now, things are OK, but afternoons are significantly busier here, so I'd anticipate things will deteriorate later this afternoon," Abraham said.
In the meantime, the FAA is considering temporarily shelving a rule that currently stops airlines from keeping passengers sitting in planes on tarmacs longer than three or four hours, to keep air traffic flowing.
The airline lobbying group Airlines for America is pushing for the option of keeping passengers on planes longer to help accommodate delays from furloughs.
Airlines want to "minimize and avoid worsening the disruption and inconvenience to our passengers," said Katie Connell, managing director for the group.
Lawmakers on Capitol Hill blasted transportation officials and the Obama Administration for not doing more to avoid the delays. On Tuesday, Sen. Richard Blumenthal, a Connecticut Democrat, demanded the administration delay all furloughs by 30 days to give Congress time to find ways to give the FAA more flexibility to avoid controller furloughs.
Also, the head of the Commerce Committee sent a pointed letter to Transportation Secretary Ray LaHood late Monday night demanding more information of how budget cuts would affect the air transportation system.
"The flying public deserves a fuller understanding of what kind of travel delays they may be facing as a result of sequester," said Sens. John Rockefeller, a Democrat, and John Thune, a Republican, in the letter.