Not sure if we are allowed to link out here, but I just read that hundreds of TSA screeners are beginning to call in sick at major airports as the shutdown continues. I'm not sure how that kind of situation gets remedied without the government re-opening. They currently aren't going to be getting a paycheck, but I don't THINK they can be fired either (I would assume that type of HR processing would be considered non-essential), nor can anyone else be hired and trained. And if this continues, major airports would likely slow to a standstill and anyone travelling within the US could be affected.
I am not sure how long it could possibly go on if air travel basically halts, especially since I'd imagine the airlines would get involved. Perhaps anyone deemed essential enough to work should be paid during a shutdown like this, maybe focus on that first and get to the rest after that's settled.