Story Highlights

• NEW: JetBlue faces more flight cancellations Thursday at Kennedy Airport
• JetBlue passengers were stuck on the tarmac at airport for 8 hours Wednesday
• Plane was like a "sound-proofed coffin," one passenger said
• JetBlue issued an apology for Wednesday's "unacceptable delays"

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NEW YORK (CNN) -- Bad weather kept JetBlue Airways passengers on a Cancun, Mexico-bound flight trapped on the tarmac for eight hours Wednesday at New York's John F. Kennedy International Airport.

Flight 751 was supposed to leave New York at 8:15 a.m., but an expected break in the weather never came, resulting in what JetBlue called "unacceptable delays" for its customers.

The airline said there were no gates available for a return to the terminal, and some of the plane's wheels froze to the ground. By 4 p.m., the plane was still sitting on the runway.

Passengers waited for hours with no movement and no information. (Watch the stranded passengers describe the flight to nowhere )

"One of the pilots should get out here and have a mini-press conference," passenger Sarah Greenberg said in a phone call to CNN as the plane sat on the tarmac. "The longer they wait, the more people are going to get upset. It's Psychology 101."

The plane was like a "sound-proofed coffin" when the windows were iced over, said Carolyn Faucher, another stranded passenger.

Greenberg said she and other passengers were getting testy because the flight attendants told them they couldn't hand out food or water until the plane had been grounded for at least four hours, citing a Federal Aviation Administration rule. At least two of the passengers were diabetic.

Another passenger said there was no power, and flight attendants had to keep opening the doors so they could breathe comfortably.

JetBlue apologized to the stranded passengers, saying they should have been taken back to a gate earlier. Eventually, three Port Authority of New York and New Jersey buses did take the passengers to a terminal.

The airline offered a full refund and round-trip JetBlue ticket for all customers whose flights were held more than three hours.

Referring to the passengers' trips to Cancun, JetBlue originally told CNN that they had located a crew and aircraft ready to go at 9:30 p.m. Wednesday, but by then the airline "was not able to communicate with the majority of the customers. Either the customers returned home or left the airport and the surroundings," said JetBlue spokeswoman Jenny Dervin.

Flight 751 was one of at least 10 JetBlue flights stuck on the ground Wednesday at Kennedy because of inclement weather, according to a JetBlue statement.

Weather problems continued to plague JetBlue on Thursday morning. Fifty-nine of the airline's 565 nationwide flights were canceled due to icy conditions at Northeast airports and the backlog of stranded passengers from Wednesday's cancellations, according to JetBlue spokesman Brian Baldwin.

Hundreds of passengers crowded into the airline's domestic terminal at Kennedy Airport hoping to board flights that should have left Wednesday but were canceled or delayed.

JetBlue said the icy conditions, coupled with the approaching President's Day holiday weekend, are complicating matters and adding to delays. Frozen planes are having to be de-iced, which takes 30 minutes per aircraft.

"We are resetting our operations from yesterday, but the added traffic for the upcoming holiday weekend is going to make things more difficult," Dervin said.

The airline is giving its New York passengers full refunds if their flights were canceled and helping rebook passengers to new flights.

CNN's Katy Byron, Brian Blank, Carol Costello, David Miller, Amy Sahba, Caleb Silver and Zak Sos contributed to this report.