ASAP is a comparatively
deferential expression, implying as it does that although you would like something done, there's no deadline so absolute that it can't be extended for a while if your
interlocutor's house is on fire, or its grandmother died, or its hair needs washing, or
Boston Kreme Donuts are on
special offer TODAY ONLY!!!.
So for those occasions when "As Soon As Possible" just doesn't seem urgent enough, or simply to impress your friends (or intimidate your subordinates) with your erudition, you should specify that it abbreviates "Aut Statim Aut Prius" (roughly translated, that's "immediately if not sooner.")