TULSA, Oklahoma - American Airlines passengers could possibly hit some turbulence during the holiday season. CBS News says a computer glitch is to blame.

"That is not a computer glitch that is a computer screw up, so they just gotta pay for it,” said John Mauldin.

Mauldin, a frequent flyer, says he'll have eight million miles with American Airlines next month.

"It’s huge for them,” he said. “It’s huge revenue. They can’t take the revenue loss.”

A union representing the pilots tells CBS news a computer glitch allowed a large number of pilots to schedule vacation from December 17th to December 31.

"We don't want the story: the Grinch who stole Christmas at American Airlines,” said Captain Dennis Tajer of Allied Pilots Association.

The Allied Pilots Association told CBS News that right now thousands of flights are at risk of being canceled.

"We're gonna have to get creative,” said Tajer. “It’s gonna require a partnership in figuring out how we get those over 15,000 flights manned with captains and first officers. It’s a heavy lift.”

Frequent flyer Joe Brown says he thinks it's an issue as well.

"Hopefully, the pilots will want to contribute to solve the problem,” said Brown.

American Airlines declined to go on camera but issued the following statement:

"We are working diligently to address the issue and expect to avoid cancellations this holiday season. We have reserve pilots to help cover flying in December, and we are paying pilots who pick up certain open trips 150 percent of their hourly rate -- as much as we are allowed to pay them per the contract. We will work with the APA to take care of our pilots and ensure we get our customers to where they need to go over the holidays."

American Airlines released an updated statement Thursday saying:

"Out of the 200,000 flights American will operate in December, only a few hundred are currently unassigned to pilots. That number of open flights continues to decrease thanks to our pilots who are stepping up to the plate and picking up trips to ensure customers are taken care of. It’s another example of why we are thankful to have such an incredible team. In addition, we have more reserve pilots on hand in December than normal months and they provide us with the ability to fly many of the trips that are currently uncovered. We have not canceled any scheduled flights in December and will continue to work to ensure both our pilots and our customers are cared for."

In the meantime, both Brown and Mauldin say American is a good airline and they believe the company will get everything taken care of.

"With eight million miles, this isn't my first glitch and they figure it out,” said Mauldin. “I'm not worried at all. My plane will take off on time."