Most Americans will quickly answer, "The Supreme Court, of course!"
Thomas Jefferson emphatically disagreed, arguing that the states make the determination in the last resort. Jefferson pointed out the absurdity of a branch of the federal government determining the extent of the federal government's powers in the Kentucky Resolutions of 1798.
The government created by this compact was not made the exclusive or final judge of the extent of the powers delegated to itself; since that would have made its discretion, and not the Constitution, the measure of its powers; but that, as in all other cases of compact among powers having no common judge, each party has an equal right to judge for itself, as well of infractions as of the mode and measure of redress.
From elementary school on, we learn that the Supreme Court gets to make the final decisions on all things constitutional. In fact, the idea is so deeply engrained in the American psyche, to assert otherwise generally elicits howls of indignant protest. But if you stop and think about it, you will recognize the notion makes absolutely no sense.
Essentially, Supreme Court apologists argue that after fighting a bloody war to free themselves from a tyrannical government, the founding generation ratified a Constitution specifically limiting the general government's power, insisted on a Bill of Rights to further define the limits on that power and ratified an amendment explicitly stating what was already implicit – that all powers not delegated to the federal government remain with the states and the people. Then, after all this, those same people gave one branch of the federal government absolute authority to interpret the Constitution.
It would be a little like letting a Dallas Cowboy player referee a game between the Cowboys and the New York Giants.
Simply put, if the federal government gets to decide the extent of its own power, through its own judicial branch, and the people of the states possess no mechanism to hold the government it created in check, the whole notion of limited, enumerated powers becomes a farce. The federal government, in practice, becomes one of limitless power.
That was not the intent of the founding generation. They never envisioned nine federal employees determining the extent of federal power. They knew that a self-limiting institution simply doesn't exist, and they would have never allowed the creation of one to rule over them.
James Madison emphatically asserted that the states retain absolute authority.
The States then being the parties to the constitutional compact, and in their sovereign capacity, it follows of necessity, that there can be no tribunal above their authority, to decide in the last resort, whether the compact made by them be violated; and consequently that as the parties to it, they must themselves decide in the last resort, such questions as may be of sufficient magnitude to require their interposition.
Further expounding on the subject, Madison pointed out that the president and Congress weren't alone in the ability to overreach constitutional authority.
The [Virginia] resolution supposes that dangerous powers, not delegated, may not only be usurped and executed by the other departments, but that the judicial department also may exercise or sanction dangerous powers beyond the grant of the Constitution; and, consequently, that the ultimate right of the parties to the Constitution, to judge whether the compact has been dangerously violated, must extend to violations by one delegated authority, as well as by another; by the judiciary, as well as by the executive, or the legislature.
Madison went on to say it logically follows that the states must retain the final say.
However true, therefore, it may be, that the judicial department, is, in all questions submitted to it by the forms of the Constitution, to decide in the last resort, this resort must necessarily be deemed the last in relation to the authorities of the other departments of the government; not in relation to the rights of the parties to the constitutional compact, from which the judicial as well as the other departments hold their delegated trusts. On any other hypothesis, the delegation of judicial power would annul the authority delegating it; and the concurrence of this department with the others in usurped powers, might subvert for ever, and beyond the possible reach of any rightful remedy, the very Constitution which all were instituted to preserve.