As air travel cancellations and delays mount during the government shutdown , affected travelers will want to consider all their avenues for recourse — including the credit card they used to book their flight .

U.S. airlines began canceling flights on Friday, in response to an Federal Aviation Administration order reducing flight capacity at 40 airports. The disruption could potentially impact hundreds of thousands of fliers.

"If you are traveling the next couple of weeks, you should expect that there is going to be some chaos and there are likely to be disruptions," said Hayley Berg, the lead economist at travel site Hopper.

The FAA estimates it handles more than 44,000 domestic flights every day. Reducing these flights in 40 airports will impact over 268,000 airline seats and

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