The U.S. military stressed in its briefing today that it's only the hydrazine that they're worried about - not the possibility that anything classified would survive reentry and could be collected by the wrong guys. The primary objective is to destroy the hydrazine tank, secondary one to blow the whole spacecraft into smaller pieces.
The satellite will be destroyed just before it would enter the atmosphere and deorbit anyway: So as little debris as possible will remain in orbit, endangering other spacecraft, and the majority comes down soon. Also the attack will take place at a point in orbit where any debris comes down in an unpopulated area, namely an ocean. The well-understood "standard missile 3" will be used, one with two backups. Three ships will be on station. Radar and space sensors will see whether the first shot hit, but finding that out could be rather tricky and take many hours.
A 're-engagement' of the target could come as late as 2 days after the first shot. "The worst is that we miss", even grazing the satellite would bring it down earlier, so "the regret factor of not acting clearly outweighed" doing something. The window for interception begins in the next 3-4 days and stays open for about one week. (Briefing still ongoing; now the NASA Administrator is speaking.)