Two magic words -- "on time" -- started appearing on some airport departure boards Tuesday as stranded passengers' patience and cash waned after a blizzard that brought transportation to a halt in the Northeast during one of the busiest travel times of the year.

For bedraggled passengers who were finally about to board flights home after Christmas, there was a sense of exhaustion that overwhelmed any excitement they might have felt.

"I don't know if I ever want to go on vacation again, honestly," said 28-year-old Tiffany Bunton, who was heading through security at LaGuardia with her 8-year-old daughter, Trystan, on their way back to Fort Worth, Texas.

Experts said it would likely take several days to rebook all the displaced passengers after the blizzard of December 2010 sucker-punched the northeastern U.S. on Sunday night and into Monday. As airports sought to get back to normal, a new snag emerged -- planes being forced to sit for hours on runways.

One Cathay Pacific flight that originated in Hong Kong and was diverted to Toronto before landing in New York sat on the runway at New York's Kennedy Airport for more than 10 hours before passengers were allowed to walk off Tuesday morning.

The weary travelers said they were given meager snacks like juice, water, cookies or instant soups, and got conflicting reports about why they could not leave. Explanations ranged from the airport not having enough staff to accommodate landings, Customs not being fully operational and a lack of gate space.

"It was so frustrating, just sitting there for hours, waiting for more bad news," said 24-year-old Gigi Godfrey of Belize City, Belize. She was in transit through New York after spending Christmas in Thailand, and didn't know what day she had first boarded a plane.

"I am so tired I don't even know what day yesterday is," she said.

Another Cathay Pacific flight from Hong Kong to New York, via Vancouver, British Columbia, sat for hours on the runway Tuesday. And 300 passengers on a British Airways flight from London spent more than seven hours overnight at Kennedy.

British Airways spokesman John Lampl said Flight 183 landed Monday night but waited until about 4:30 a.m. for an open gate. By that time, Lampl said, Customs officials had gone home for the night, and passengers had to remain on the plane until more Customs workers showed up at 6 a.m.

As travelers inside the airports saw more flights opening up, they still had long travel nightmares ahead.

Adriana Siqueira, 38, a housekeeper from Fort Lauderdale, Fla., has been told she and her 10-year-old daughter cannot get home from New York's LaGuardia until New Year's Day. They have already spent one night in the terminal and can't afford a hotel.

"I have no idea what I'm going to do," Siqueira said. "I don't feel good."

In New York, residents outside Manhattan complained of a sluggish response by plowing crews who still hadn't finished clearing the streets. Fire officials said the unplowed streets and abandoned cars made it harder to respond to emergencies, including a five-alarm, wind-whipped blaze at a Queens apartment building Monday night.

Mayor Michael Bloomberg said Tuesday that hundreds of city buses and dozens of ambulances remained stuck in the snow throughout the city, and officials predicted streets would not be clear for another 24 hours, a day later than they first promised.

"The bottom line is, we're doing everything we possibly can and pulling every resource from every possible place to meet the unique challenges that this storm is posing," Bloomberg said.

Bloomberg said the city simply does not have enough tow trucks and crews to dig out the abandoned vehicles, and has been pleading with private companies to help out.

Some 1,000 vehicles have been removed from three major New York City-area expressways alone, he said. Emergency vehicles erred in trying to navigate unplowed streets during the storm, and New Yorkers also should not have ignored warnings and driven during that time, he said.

The Fire Department said it received more than 4,000 calls during the storm — its busiest day in recent memory, apart from the Sept. 11 attacks.