Despite a fairly straightforward definition the phrase "as soon as possible" is no longer very helpful when used in conversation. According to the definition, ASAP is designed to be used in situations where you should drop everything and run to complete the referenced request AS SOON AS POSSIBLE. Unfortunately, in my daily encounters with ASAP requests people are not using it with any of the urgency with which it should be associated. People will often ask me to get them an article ASAP, but when I tell them I can have it in an hour for a cost of $20 (paid by me, not them) or they'll need to wait a couple of days they almost always choose to wait. I've even sometimes had to wait weeks for books on loan, but even though the requester asked for it ASAP they had no problem with a wait of a few weeks. On the other hand, some people will ask me to find them a list of 10 or 20 articles and then be surprised that they take more than a day to round up. Those are never the same people who request things ASAP.
What most people are really asking for when they say ASAP is that I simply don't ignore their requests for days or weeks before getting to it. That's a reasonable expectation, but also an expectation that I would comply with even without the unnecessary use of ASAP in the request. If you have something that needs to be done within a certain amount of time then let me know what that actual time frame is and I can decide whether or not I need to rush, but don't just throw ASAP around willy nilly because by now I've learned not to pay it much heed.