"You are trying to put them on planes that are already packed. There isn't a lot of room to re-accommodate folks," AirTran Airways spokesman Christopher White said.
AirTran is hoping to return to normal operations by late Wednesday or early Thursday.
Those with confirmed tickets for flights Tuesday, Wednesday or Thursday typically get priority over passengers whose flights were canceled earlier in the week.
New York's three area airports restarted some operations Monday night.
LaGuardia Airport officials in New York said they planned to open a second runway Tuesday morning.
For airlines, the problem might not be whether planes can take off and land but whether there will be enough staff at the airport to load baggage, take tickets and do security screenings of passengers.
Ed Martelle, an American Airlines spokesman, said the airline put up a lot of its staff near the New York airports in anticipation of the storm. But as shifts change, it might still be hard to get replacement staff to the airports, given the poor condition of the roads.
"Can they get there? That's a huge question right now," he said. "It's like trying to do a jigsaw puzzle but the pieces keep changing. This is just phenomenally complicated."
Take American Eagle's flights between New York's LaGuardia and Detroit. One of the planes used on that route was diverted overnight to Rochester, N.Y., because LaGuardia was closed. So before a new group of passengers could board the plane to head to Detroit, that aircraft has to leave Rochester and make it to LaGuardia.
The blizzard is probably going to cost airlines several million dollars in overtime, lost revenue and other storm-related expenses, such as de-icing planes. Airlines said they were focused on getting passengers up in the air again and didn't yet have an estimate on costs.
But if a December 2006 Denver blizzard is an indication, it won't be cheap.
Denver International Airport was closed for 45 hours by a storm that started Dec. 20. 2006.
More than 2,000 flights were canceled and about 4,700 travelers were stranded.
United Airlines said it lost about $30 million in revenue because of that storm, and Denver-based Frontier lost $13 million.
New York is home to many lucrative international routes, especially for American, Continental and Delta, making the losses greater.
Henry Harteveldt, an airline analyst with Forrester Research, noted that airlines budget for such storms.
"This happens every winter. It also happens every summer when you have thunderstorms in certain markets," Harteveldt said. "It's part of the game."
Stock prices for the parent companies of United, Continental, American, Delta and JetBlue -- all with a large Northeast presence -- were either flat or up today. US Airways was down but only slightly.
Most airlines have taken the highly unusual step of giving passengers the ability to rebook flights within a 14-day window of their original plans. Usually, it's only three or four days. That should help spread out rebookings slightly.
For airlines, the test comes in how well they communicate with their customers about the delays.
"This is where an airline proves itself," Harteveldt said. "It's been known when an airline doesn't do a good job in something like this they lose customers for life."