I don't know the specific laws but making a threat in person, phone on internet is an assault. I would assume there are laws for threatening a large group of people too. But if that had been followed through there are still limits to how long you can lock someone up. Maybe it would have slowed him down or made it harder get armed, one would think.
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So, you have to be more clear. Assault in some states is merely a threat. Other states view "assault" is the same as "battery" in Florida therefore the definition and application of assault in fact varies. In FL thought, assault is the threat not touching component, which requires 1) threat to be made 2) Fear or concern of harm to the potential victim and 3) ability to carry out the threat. And I am not a lawyer, but I do know a fair amount about the application of FL Statue 784.011. If he is just typing on the internet and that ended up with an charge and arrest of "assault", the lawyers would have a field day with poking holes as he didn't meet all the requirements in Florida. Lack of specificity in victim and exact method, ability to carry out that specific threat (there is a time component, he didn't rush right over to a location), who was in fear of their safety. With no effort, I just created 3 obvious holes in the charges you want to see......
Now I don't know what the Federal laws are in regards to general terrorist threats nor the Federal laws they leverage when they investigate and charge people for threatening politicians. But in summary, no, making a threat, as you indicated above in this way, is not assault.
Now that said, do I think the Feds failed? Yes, obviously. The lack of investigation of a threat seems clear. Could they have done something if they had investigated? Possibly. Are the laws (state and federal) out of touch with current environment? Clearly. Will we see changes? I would expect so. Does that help the current victims and families. Not one effing bit.
There are Baker Act rules, but those are only for self harm and mental health issues, he doesn't seem to fit into that category BEFORE this episode.