No, the specific problem is that Americans can't comply with GDPR because they are American.
This will be the state of EU law until America either repeals the CLOUD Act and shuts down the NSA, or copypastes GDPR into local law. I would prefer either to be honest.
The CLOUD act is one thing, but Section 702 of the Foreign Intelligence Surveillance Act is a far bigger problem. Allowing the FBI, CIA and NSA full access to all data regarding every non-American without a warrant required on every US internet service is a massive breach of privacy, and will always be a GDPR breach.
I'm not sure this is correct. The EU and US agreed "in principle" on a new privacy shield in the spring of this year [0]. Maybe third time is the charm? (I think this is the third attempt.)