Good points, you also reminded me of another claim I've seen about how as soon as the Federal government "really starts to shut down", mayhem will ensue, like food safety issues will arise and cause the GOP to abruptly about-face. It is more nuanced than that, and the GOP can release highly-targeted funding bills that paint the DNC into a corner.
If air traffic controllers start to quit for example, and air travel starts to shut down, then as a stopgap if it isn't a wide enough impact, Trump can order the armed forces to help direct air traffic. If it is a big enough impact, then the GOP can allow for a targeted bill just for the air traffic controllers. The DNC then finds itself in an unenviable position. Block the targeted funding bill just for the ATC's, and the mayhem squarely lands on them. Allow it to pass, and they start losing political points in this dominance game. It's not good optics for the DNC either way.
For some issues like food safety, we're not going to run into PRC-level, pre-FDA era food supply chain adulteration overnight, many fiscal quarters and years is more likely. It took decades in the PRC before the adulteration got to the levels we see today, and they still don't experience political unrest from it. The longer this shutdown runs, the more ammunition the DNC is handing GOP "small government" advocates' rhetoric (as over-caricatured as that rhetoric will be, and as wrong in its over-simplification it is, it will play well to the GOP base). The GOP wet dream is the shutdown drags on indefinitely, and they get to "starve the beast" by reverse-budgeting: find out what part of civilizational collapse becomes unacceptable due to lack of operations, fund only those parts, and devil take the hindmost. That's like a nightmare scenario for the DNC.
It can get worse, too. ATC example above: Trump orders a vestigial FAA to tell everyone using airspace they now can only access airspace if their special usage-tax is fully paid up, and budget all critical FAA functions via pure utility revenue collections. Or designates a private company to administer the airspace management, who collects revenue, and is granted by executive power the ability to regulate access to airspace, and disband the FAA. The salivating within GOP think tanks is almost audible.
The DNC appears to my casual observation to be playing right into the GOP's hands. I'm far, far from some kind of politics wonk/hacker, though. So I'd sure like to be shown a way out of the DNC's dilemma by political hackers who follow this stuff much more than I do.
I think if the DNC can put together a two-plus year budget plan in exchange for caving on the wall, then they take this corner they've been painted into out of the GOP's hands. By no means should the DNC accept temporary budget bills for just a month or so: that just loads more bullets into the chamber to shoot the DNC with more shutdowns.
By refusing to compromise ($5.7B is about a quarter of the estimated $25B entire wall project), the DNC backed the GOP into a corner with their base, where the GOP politicians got nothing to lose by pushing back. By raising the stakes into "for all the marbles", the DNC told these GOP politicians they have nothing to lose by demanding the entire $25B instead. If the DNC is going to play that kind of hardball, I sure would love to be a fly on the wall to hear what their strategy is.