I suspect they hope to rely on the usual "diplomacy"
The US has never really negotiated, usually it has amounted to arm twisting by threatening with either trade regulation or not paying back some of the massive debts they are still running up every minute (which implies that any action that allows more debt creation ought to be blocked, but I digress)
Given that in Trumpism it considered it an "art" to have a winner/loser outcome instead of negotiating, I can't see that approach improve, so it depends on just how solid the EU wants to make a stand for privacy.
Legally, the US hasn't got a law/leg to stand on.