Ancient Greek:
Oxus = "sharp"
Moros = "dull"
"Oxymoron" = a sharp dullness or a foolish wise...a self contradicting phrase.
Personally, I think that "drink responsibly" is an oxymoron just as much as "jumbo shrimp", "civil war", or "holy crap" are.
What is a DWI? Driving while intoxicated. (DID YOU NOT SEE THAT LAST PART!!) Here's a known fact: alcohol is a toxin. Simply put, by drinking people are intentionally poisoning themselves. Does that sound responsible? Are you treating your body responsibly if you eat a bit of rat poison on the weekend "just to loosen up"? NO, and neither is it possible to intoxicate oneself "responsibly" with other poisons.
Our bodies try for hours and hours to purge itself of the toxins of alcohol. If you are to be responsible (able to respond), to others, your environment, and even to your body (as in able to make quick, rational, and conscious decisions), you will not put toxins into your body that will impair your judgment.
I'm not MADD, I'm reasonable. There is nothing responsible about drinking.
Just a side note: I'd rather be an oxymormon = "sharp" "mormon" :) haha!

Here is an ad campaign that seems to think it is possible to drink "responsibly":
http://theinspirationroom.com/daily/2008/guinness-traffic-signs/