It takes a while just for people to not get paid.
The government shut down end of day the first of the month. Anyone on a monthly pay basis doesn't give a fuck that they get a free vacation for however long this lasts unless it actually goes longer than a month. Even bi-monthly pay basis still gives a solid two weeks before the economy would even notice people not getting paid.
Veterans with disabilities not getting paid is just scare tactics. The VA is still operating, they aren't even closing hospitals. Some asshole Senator said they might have to short check or delay payments, as if he had any clue what he was talking about, or any reason to be honest, and the news ran with it. They've already stated that they have funding through most of the month. If anyone expects either party to last a month on this, I'd love to hear their reasoning on how a bunch of spineless shits that didn't even go to the wire the last time around are going to survive a month of the media laughing at them. Thoughts of the media running around to the homes of people that had their legs blown off in Iraq and Afghanistan not getting their disability pay would have them all losing their sanity from sleep deprivation before they hit day zero.
As to the market compensating for government disappearing, this is a misconception of what government does. Government gets in the way, it does not facilitate.
Government inspects cargo coming into the US, no inspectors means no inspections. No inspections does not mean no cargo, just that the minute percent of them getting inspected now wont be. Government inspect food production, no inspections once again just means no inspections. In this case it's even less useful because government inspections have a bad habit of never actually inspecting until after someone gets sick. Until someone does, inspections consist of an inspector walking into a factory, looking around briefly, and then leaving. They don't even swab something to see if the surface of processing equipment is actually being cleaned, or nobody would ever get sick from eating contaminated peanut butter shipments.
Transportation is unaffected. Customs is still operating all critical services, the FAA is still operating all critical services. The FDA isn't even shut down, nearly all of the above inspection services are still taking place. We basically still have a fully functioning government with their fingers involved in far more than the libertarians would like. Most of what we've lost is access to a bunch of gated parks and federal buildings.
This only poses some kind of problem if it runs a month plus. If we weren't such an irresponsible society that lived from paycheck to paycheck with all our credit cards maxed, it wouldn't be a problem even then.