This bill would do absolutely nothing at all legally. Here is the operative part of the bill:
The Fourth Amendment to the Constitution shall not
be construed to allow any agency of the United States
Government to search the phone records of Americans
without a warrant based on probable cause.
The 4th is part of the Constitution. Congress cannot change its meaning with a mere bill. Changing the meaning requires a Constitutional amendment. So, no effect from Paul's bill as far as that goes.
The courts interpret the Constitution, and due to separation of powers, Congress can't tell the courts how to interpret it. So, no effect from Paul's bill here, either. Separation of powers also prevents Paul's bill from having any effect on the executive branch.
To make this sort of thing work, I think you'd have to go to the laws that actually created or authorized the agencies whose behavior you want to change, and amend those laws.
Can't you straighforwardly strike the "Fourth Amendment... construed" part and leave the core "no agency of the US government... [shall]"? Because that's be solidly in the purview of Congress. And my flimsy understanding of law is that, if SCOTUS were to look at this, they would do something like what I said -- respecting the intent of the legislature as closely as possible -- rather than throwing out the whole thing.
I think this bill isn't expected to pass anyway, so it makes sense if it's been optimized for rhetorical, not legal, power.
The courts interpret the Constitution, and due to separation of powers, Congress can't tell the courts how to interpret it. So, no effect from Paul's bill here, either. Separation of powers also prevents Paul's bill from having any effect on the executive branch.
To make this sort of thing work, I think you'd have to go to the laws that actually created or authorized the agencies whose behavior you want to change, and amend those laws.