Internal Revenue Services (IRS) employee Matt Westrich speaks in front of the Federal building at a rally against the ongoing U.S. federal government shutdown, in Ogden, Utah, U.S., January 10, 2019.

"In our risk averse industry, we cannot even calculate the level of risk currently at play, nor predict the point at which the entire system will break," said a joint statement from unions representing U.S. pilots, flight attendants and air traffic controllers. "It is unprecedented."

The partial government shutdown is straining air travel and posing safety concerns, aviation unions said, while airlines warned travel disruptions could worsen if the impasse isn't resolved soon.

The shutdown, which began Dec. 22, has left federal employees like the 51,000 Transportation Security Administration officers who screen luggage and passengers at the nation's airports without pay. TSA officers, air traffic controllers and a host of other government employees from FBI agents to government food inspectors, are among the some 420,000 employees who have been deemed essential and ordered to work without pay. Other government workers have been furloughed.

Internal Revenue Services (IRS) employee holds signs in front of the Federal building at a rally against the ongoing U.S. federal government shutdown, in Ogden, Utah, U.S., January 10, 2019.

Travelers have already faced long lines at some of the country's largest airports, as unscheduled absences of TSA officers surged. The agency said some of its employees haven't been able to come to work due to financial strain.

Federal Aviation Administration spokesman Gregory Martin said that the national airspace is safe and that the FAA has seen "no unusual increased absenteeism and there are no operational disruptions due to staffing." The agency also has not seen a rise in unplanned air traffic controller retirements and resignations, he added.

Yet the longest-ever shutdown is already denting revenue at some of the country's largest airlines. Southwest said Thursday that it lost up to $15 million so far this year, while Delta Air Lines last week said the shutdown cost it $25 million in revenue this month as fewer government employees and contractors are traveling.

The amounts are small considering airlines' revenue. Delta alone generated close to $11 billion in the last three months of 2018. But the impact worrying the industry since there is little indication that the shutdown could be resolved in the near future.

American Airlines said it has seen some weaker last-minute bookings but declined to provide a dollar amount. The carrier expects to its revenue to grow in the first quarter by as much as 2 percent.

But the airline's CEO Doug Parker said the carrier is concerned about travel disruptions the longer the shutdown goes on, particularly if absences of federal airport safety workers pick up.

"It certainly means longer lines at airports, it means less efficient travel through the airspace," Parker told CNBC. "It's going to have a huge impact on air travel before too long if we can't figure out how to get this resolved."