Comment by OkayPhysicist

This is true in this case, but in general complicated in the US. Since the executive branch is responsible for diplomacy, but only Congress can pass laws, there's a weird wiggle room where the Executive branch is completely on board with signing some treaty, but then when it comes time to actually implement it in any way that actually binds, Congress can refuse to do so.

It's one of the reasons why for a lot of the "everybody joins" treaties, a bunch of countries sign with a statement that they don't recognize the US as a signatory.