In some sense, this reminds me of some things that I heard right after the Tuscon shooting. There was talk on the TV of making it illegal to possess a firearm within 1000 ft (IIRC) of one of our members of Congress. One of the problems that I saw with that was that it would have created "roving gun-free zones" with no notice to the public as to when or where such a zone might exist. If this bill functions as the article claims, it looks like it might create "roving protest-free zones."
I'm a lawyer, but I'm not your lawyer. If you need some honest-to-goodness legal advice, go buy some.