Paxton explained the difference between what he called the "normative state" and the "prerogative state." What this means, as I understand the difference, is that while modern governments carry out a large host of functions, only some of those functions are genuinely political in nature--and the prerogative state pertains to those heavily political functions while the normative state pertains to the non-political (or marginally political).
For example, even in Vichy France it was presumably necessary for various government agencies to do things like deliver the mail, regulate meat plants, inspect coal mines, etc. I suppose one could easily use his or her imagination and come up with ways that a Vichy mail carrier might do the job differently than a free French mail carrier, or how Nazi meat regulations might differ from ordinary meat regulations, or how a Vichy mine safety inspector might assess dangers differently from other mine inspectors, and so on. But for the most part, mail is mail Meat is meat. A coal mine is a coal mine. These are normative state functions. So except maybe around the extreme margins, having a Vichy government doesn't really feel much different than any other government with respect to normal, everyday functions.
Then you have the prerogative state. These are going to be the things deeply politicized in a given society (often any society). The content of education. Policing. Foreign policy. Immigration and naturalization policies. Civil rights. Freedoms of expression, press, assembly. Voting rights. Certainly there is much more--but these are the prerogative state issues that truly reveal the character of a government. These are the areas where having a Vichy regime rather than a true democracy truly manifests.
Whether the chief executive of a republic is subject to that country's laws is obviously a core prerogative state question. It has historically been fundamental to this's country's notion of itself as a democracy that the answer to that question be yes. One whose rights need not be respected is not a citizen, but a slave.
When the Senate fails to accumulate the necessary number of votes to remove Donald Trump from office, despite copious evidence that he abused the office for personal political gain and then repeatedly lied about having done so, it will effectively establish that no, the POTUS is not subject to the country's laws. The POTUS is, in effect, a king who may do what he pleases. The essential yes will have become a no.
Things may not feel much different the day after that happens. The mail will still be delivered. Meat plants will still be regulated. Coal mines will still be inspected. We likely will not feel as though we've become slaves--certainly not in the sense Roger Taney was writing about.
But we should not dare presume that we remain citizens. One is only a citizen if his or her rights must be respected.