First off, in the Constitution, the Courts are NOT given that mandate. The scope of judicial power is specified:
Section 2. The judicial power shall extend to all cases, in law and equity, arising under this Constitution, the laws of the United States, and treaties made, or which shall be made, under their authority;--to all cases affecting ambassadors, other public ministers and consuls;--to all cases of admiralty and maritime jurisdiction;--to controversies to which the United States shall be a party;--to controversies between two or more states;--between a state and citizens of another state;--between citizens of different states;--between citizens of the same state claiming lands under grants of different states, and between a state, or the citizens thereof, and foreign states, citizens or subjects.In the Constitution, itself, no one is named as the final arbitrator of Constitutionality. Why? because like the rest of the balance of powers innoculative princible, so too was the right and duty to interpret Constitutionality. As Jackson said -- "bring their army!" (Paraphrased.)
The maxim that the US Supreme Court is the master of the Constitution is, in a way, challenged by that exceptions clause you mention. In that it almost appears -- a suggestion -- that it is Congress who is supreme. Yet even that is not so, for the very first words are "We, the People" -- the People are in the first by initial charter, and in the last by the continuation of their sufferance for it, or parts of it -- the bottom line masters of the Constitution.
And we have the States and the Executive also, as claimants to that authority at the same masterly tier -- so they are! The Civil War showed both in their Master's Robe. Where were the Court's armies? None! The Court survived because the Executive, as Commander-in-Chief, and its forces bested some of the States in vicious, long combat. At any time -- as the length and blood of that War makes clear -- it could have gone for the States. The point being made resoundingly. The National Executive and the States are both at equal level in determining Constitutionality.
Today in our silly and amoral times, the Court is ascendant, by the insane actions and inactions of the Natonal Legislature and the States and the go-along-ism of the Executive. The People -- they are coddled, sheeple, shy. But in a few weeks -- that's all it would take -- they could rise up like lions asserting every masterly perogative like a Tidal Wave asserts its perogative over a city by the sea.
Such few weeks would be tumultuous -- full of terror and horror and calamity to cause the People to so rise up. Would that they be able to rise up sans the physical and emotional terrors and rather on the basis of refined spirituality, morality and intellect.
They would form a Convention -- by the Constitution or without it -- and either take it back into the Founder's ideals for it, or cast a new one.
We have seen when the State legislatures pass consenting proclamations -- that is how we have modified the Constitution to date. We have not yet experienced a Constitutional Convention besides the first, that of the initial charter. Yet without such a national meeting we will fall into tyranny, decay, and death as a nation.