That's exactly what we're already talking about here: companies are unable to obey both EU rules concerning privacy, and US laws concerning law enforcement access to data.
And that's basically why borders between internet jurisdictions are now being drawn up.
> The Court adds that legislation permitting the public authorities to have access on a generalised basis to the content of electronic communications must be regarded as compromising the essence of the fundamental right to respect for private life.
> Likewise, the Court observes that legislation not providing for any possibility for an individual to pursue legal remedies in order to have access to personal data relating to him, or to obtain the rectification or erasure of such data, compromises the essence of the fundamental right to effective judicial protection, the existence of such a possibility being inherent in the existence of the rule of law.
http://bits.blogs.nytimes.com/2014/07/31/judge-rules-that-mi...
http://arstechnica.com/gadgets/2015/09/report-google-will-co...
This is a problem for the internet that has long been present but is increasing: multiple jurisdictions with global reach. Historically the First Amendment has shielded the internet from a lot of attempts to interfere with it, but there's no particular reason why only the US should claim that its laws apply globally. Why not Franco-German laws against Holocaust denial? English libel law? Saudi blasphemy law? Chinese censorship law?
Sooner or later someone's going to find themselves in a Kafkaesque situation where two global jurisdictions demand incompatible things.