It actually may, and this is something being debated in the courts.
http://blogs.wsj.com/law/2016/07/28/judge-first-amendment-pr...
http://blogs.wsj.com/law/2016/07/28/judge-first-amendment-pr...
However, a key sentence from the article was:
"concrete plans to accelerate the development and adoption of new tools and solutions,"
The "new tools" doesn't sound like crafting a law for a court to strike down but new technology to empower users to block the nuisance calls.