I recently heard an old Motown hit on the radio called "Shotgun" by Jr. Walker and the Allstars and the Sax part tore me up. It sounds to me like it's seriously overblown, but I don't play sax so I really don't know what I'm talking about. I would like to know if there is a term for this technique and how it is actually accomplished, anyone?
This effect is usually called a "growl". There are two techniques (as explained in the linked video). The one in "Shotgun" is most likely the "'growl' in the back of your throat while playing" technique. The other technique is to hum while playing. When humming, the more consonant the hummed and played pitches, the smoother the growl; the more dissonant, the "growlier".
I suggest you consider one of the many YouTube instructional videos. Like this one, for example (chosen because it's short)...
Websites like TamingTheSaxophone also include instructions and practice tips (humming in this particular case).
These techniques work on most, if not all, wind instruments. (I can personally attest to the trumpet.)
Growling is an example of a larger set of extended techniques called multiphonics. Wikipedia has a very good article introducing the subject, describing its application to winds, brass, strings, and voice, and providing some history of its use, including a list of composers and musicians who employed the techniques. Based on the article, here are a few historically important uses (videos are timed to an appearance of the technique).
- Early usage in Western Classical music: Concertino for Horn and Orchestra in E minor, J188 (Op. 45) (1806, 1815), by Carl Maria von Weber (SCORE: IMSLP, see m. 168.)
- Illinois Jacquet popularized the technique in jazz beginning in the 1940s: "Flying Home" (1942), by Benny Goodman and Lionel Hampton.