The call is actually for most all of the aviation industry to walkout. Aviation workers, check. People that count on medicine that is shipped, check. All federal workers currently working without pay, check. It's a scary call, but it's one that would have an immediate, obvious impact on an already shaky economy while over a million are either furloughed, working without pay (but expecting to get paid after the shutdown ends), and federal contractors, whose back pay may very well not happen.
If this were to actually happen, what would that look like?
1) All commercial and private flights would be cancelled until the shutdown ended. This is obviously the biggest impact, especially with a little thing called the Super Bowl less than two weeks away. Additionally, it could potentially ground UPS, Amazon, and even USPS cargo flights, as those planes still rely on air traffic control and other services provided by airports. So in addition to screwing with everyone's travel plans, leisure or business, public or private, it would have a massive impact on commerce in general.
2) It would piss off millions and millions of people. Seriously, it doesn't matter if you're a Prime member now. If the warehouse isn't local, it's going to be a bit before you get your order. And that goes for nearly all shippers. That important medicine you need? We're sorry, but the shutdown is preventing us from getting it to you. Still paying your bills through the mail? Those may not get there on time.
3) It would bring this entire debacle upfront and center, and every single poll shows that the majority of Americans know this entire thing involves Trump and McConnell. There is no hiding for them anymore. They are the only two, and I mean that sincerely, that are blocking an end to the shutdown. The House has passed several bills that would reopen the government. McConnell won't allow a vote on any of it because he says Trump won't sign it. Think a near complete halt of air travel and commerce might change their mind?
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I have no idea if this will actually happen, but I did spend some time researching whether or not it would effect private as well as public flights (it will -- see the source material linked above). I wondered if it would effect shipments (it will -- even private fleets rely on airports, and if no one is at the airport, they're SOL). The medical example is from the source linked above.
It would be a shitstorm of massive proportions, and even just 24 hours of it would cause a massive uproar the likes of which haven't been in decades.
It seems like an extreme measure, but at the same time, I'm not sure if there are any more reasonable measures left. Reason was thrown out the window in January of 2017.