I wonder how this policy would interact with something like the Posse Comitatus Act.

Would it effectively require applying the label "terrorist" or "national security threat" to any criminal who shows they are prepared to use lethal force against a law enforcement officer?

Yeah, life isn't "Die Hard", if someone is using "high caliber armor piercing guns" against the local PD, then classifying them as "domestic terrorists" and calling in specialists to deal with them seems appropriate to me.

Police have to deal with enough crap that they shouldn't be expected to handle paramilitary situations as well, is what I'm saying.

As a counterexample, remember the "Bundy standoff"? https://en.wikipedia.org/wiki/Bundy_standoff That's the kind of situation where the Posse Comitatus Act means you don't send in the Army. However, if they had shot a bunch of people I'm sure they would have had to face at least the National Guard, eh?