In practice, in America, the Supreme Court has a final say. Knowledgeable advocates of the position Steve Hays mentions continually rue this. For example, Ed Whelan, as quoted by Steve Hays in an earlier post, states: "We live in a legal culture besotted by the myth of judicial supremacy." And again: "Although there are some scholars, both on the right and on the left, who challenge it, most lawyers across the ideological spectrum, having suffered the detriment of a modern legal miseducation, embrace it." In other words, Whelan's position is a minority position that reflects the way he thinks the system should be not the way the system actually is.
That said, I don't think any of the arguments for Departmentalism are very compelling. For example, Whelan argues (quoted by Hays):
It is one thing for the Supreme Court to decline to apply a law that it deems to be unconstitutional; it is quite another for it to maintain that presidents, members of Congress, and state officials must likewise regard the law as unconstitutional and, further, must accept and follow the rationale of the Court’s decision.Whelan is whiffing. There are at least three strikes there.
1) Although in some cases the Supreme Court decides whether something is unconstitutional as applied, the Supreme Court often decides whether something is unconstitutional on its face, and consequently void. Whelan tips his hat to this point, but doesn't seem to realize its far-reaching implications.
2) Not all of the Court's decisions relate to the Constitution. Sometimes the question requires interpreting a piece of legislation and deciding what the legislation means. We'll come back to this issue shortly.
3) In America, no one has to "regard the law as unconstitutional" (in the sense of agreeing that the Court decided rightly) nor must they "accept and follow the rationale" that the Court offered. They are free to think the Court decided wrongly. However, even if they disagree with the ruling, they have to obey the ruling until it is overturned. That's true whether it's a really controversial Constitutional issue or a less controversial legislative issue. And that is how the system works. It's easier to overturn decisions about the meaning of statutes and much harder to overturn interpretations of the constitution. But the same rule applies.
According to Whelan, the Court didn't come up with judicial supremacy until 1958. That kind of claim runs face-first into a more complete history of the situation (see here, for example). Famous cases along the way include the Court striking down the original income tax law, leading to a Constitutional Amendment to overturn the court's decision.
The most bizarre part of Whelan's argument is this: "But none of this speaks with clarity or force to the judicial-supremacist claim that other governmental actors must abide by a federal judge’s view that a law is unconstitutional." What would be the point of having a judiciary that no one had to obey? The idea that the Supreme Court's decisions on constitutional matters are just advisory is just nuts. One doesn't have to agree with the Court, but one does have to obey the Court.