Just because it goes by the name of a "treaty" doesn't mean it will be treated like one.
The DMCA, originally a WIPO treaty, was treated like a regular law and only require 50% of the House and Senate to become law. Not just that, they also often use a technique such as a "show of hands" (aka voice vote) to pass controversial legislation in secret.
Using this technique there will be no way to know which Congresscritter voted for or against the regulations, reducing their accountability and making the number of Congress in favor of the bill unknown. This also occurred for the DMCA.
The Constitution in general is a worthless document. It's the monarchy of the USA, respected but with no real power. It hasn't been actively enforced since FDR and the "living document" assertion. What really matters is what the Supreme Court says the Constitution says, not actually what it says.