The union says controllers missed their first full paycheck this week and are urging passengers to pressure lawmakers to reopen the government.
"Every day that this shutdown drags on is going to add an element of safety risk into the national airspace system," said Charles Jacques of NATCA.
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Jacques said the financial strain is compounding the already high-stress nature of the job, with controllers now distracted by missed pay and mounting bills.
"I now have people coming to work every day not receiving a paycheck, now wondering, 'How am I going to pay my bills?'" he said.
Travelers expressed concern over the situation.
"There's a lot of concern; safety obviously is number one and paramount. And people need to eat - the holidays are coming," said Jo Ellen Roder of Bayville, New Jersey.
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Transportation Security Administration workers are also feeling the pressure. TSA Union President Joe Shaker said employees are struggling to afford child care, gas, and tolls just to get to work.
"On a scale of one to 10, it's probably negative two," Shaker said. "They're going to come to work until they can't. Simple as that. Until they are faced with a choice of, 'I gotta stay home with my children,' or 'I don't have gas for my car.'"