In an American context, it would be absurd to close all US schools just because of a general warning somewhere in the country. And, to be fair, a population of 316 million is a lot more than 17 million.
Though, I couldn't imagine all state schools being closed, either, even if a threat was isolated to a single state. Hell, I'll say the same thing for a county.
I've had school cancelled once for a threat in my life, and it was a bomb threat written on a bathroom wall in one of my schools. When the township next to us had a threat in a regional school (that served some of my town's teenagers), they just stationed a bunch of police officers in the schools - patrolling, at all entrances to the buildings, and to the grounds (if applicable).
Anything else, and there's almost no chance we'd close. Though that might change based on proximity to other events. If a threat was made today, it would have a much bigger impact due to how recent the Boston bombings and Sandy Hook were.
Anyways, you all are horrible, @#%^ed up people