"although whether a treaty trumps the Constitution is a very murky area" says the article (not Jack Gregson, the article itself).

Article I, Section 10, of the Constitution forbids the states to enter into a "treaty, alliance, or confederation," although they may enter into an "agreement or compact" with other states, domestic or foreign, but only with the consent of Congress.

Is that clear enough for everyone? But even if you ignore this, Senate mega-approval is still SOOOOOO required:

Article II, Section 2, Clause 2, of the U.S. Constitution gives the president the power to negotiate and ratify treaties, but he must obtain the advice and consent of the Senate (in practice solicited only after negotiation); two-thirds of the senators present must concur.

Even clearer?