[MamaTexan]

The Supreme Court has no such constitutional authority.

Yes, it does.

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 forever, and beyond the possible reach of any rightful remedy, the very Constitution which all were instituted to preserve.
James Madison, Report on the Virginia Resolutions

The case of Marbury vs. Madison fell squarely within this authority since it was a case that concerned the executive and judicial branches of the general government.

[Doug Loss]

First, Madison's opinion here is not part of the Constitution. Now that that's out of the way, you misunderstand what he wrote anyway. He said, "in all questions submitted to it by the forms of the Constitution." This means in all things the Constitution says in in the purview of the Supreme Court. It quite specifically doesn't say that ruling on the constitutionality of legislation is within that purview. What Madison says here is that the Supreme Court's rulings can't be overturned at the whims of the Executive or the Legislative branches. If you read the proceedings of the Constitutional Convention, you'll see that the Founders debated whether to give the Supreme Court authority to rule over the constitutionality of legislation and rejected that idea. Marshall usurped that authority anyway and no one stopped him or the succeeding Courts.