Free Speech has always had some restrictions - you can't just say whatever you want, whenever you want. These are known as "time and place" restrictions.
A notable case - The Supreme Court upheld a ruling against anti-gay activists who protested at a fallen soldier's funeral. They basically showed up with signs that said the dead soldier was the result of gays in the military and it was God's wrath upon the dead soldier. The activists were removed but they filed suit stating their right to Free Speech had been violated. The Supreme Court has, on numerous occasions, upheld time and place restrictions. This example was no exception. This is also why protestors at political rallies are blocked off - they can protest, but it must be in a gated area away from the main traffic.
I hate it when people insist this is a free country and they can say whatever they want. There is a time and place for everything. Let's be reasonable here folks.
Now, about this bill. I would see some correlation to precedent in that this new bill seems to clarify some of the time/place restrictions of past rulings, but it will be very interesting to see how the Judiciary will react if and when an issue arises (if this bill even passes). There are some issues with the bill that, in my mind, would get it struck down - the whole being punished for protesting around a government official you didn't even know was there is kinda over-reaching, and as past rulings have shown, the Supreme Court does not like over-generalized laws/statutes...
I don't see this bill doing much accept being fodder for people right now... it's hyperbole...