Yes, I know, today is Friday, and I promised a KN^4 post, but 1) those take a long time and 2) since I am facing something of a 絶体絶命 situation myself right now (ok, that's a little bit of an exaggeration), you'll have to do with another topical yoji. As an added bonus to make up for the lack of KN^4, this is actually a useful yoji that will likely make your 言い回し more 日本人ぽい, instead of the normal ones that really only serve to make it 語学オタクっぽい.
This yoji derives much of its meaning from the individual characters, so, as always, that is a good place to start.
絶, which appears twice, means to end, to suppress, or to be cut off. 体 is body; 命 is one's life. Note about 命: Japanese has a number of characters/words that can be translated into English as "life." Though this is a Japanese Language Trivia Post/KN^4 post of its own, just be aware here that "life" what we might think of as the quality of being alive, as opposed to the quality of being dead. Hence, you get such phrases as 命ある限り "as long as I am alive," etc., etc. Note also that although 絶体絶命's first two characters are pronounced as 絶対, they are NOT the same. Hence, 絶対絶命 is wrong. Some cursory research has revealed that 絶体 and 絶命 were also the names of "evil stars" in a specific kind of Chinese astrology (九星占い, for those of you interested in firing up those google skills).
So you can think of 絶体絶命 as a situation that is so difficult to deal with that both your 体 and your 命 end up 絶-ing. Which brings us to our:
1) to have one's back to the wall
2) to be between a rock and a hard place
3) to be in serious trouble
Tomorrow is the deadline for my paper, and then the day after tomorrow I have an important interview, and on top of all that today my teacher asked me to help with his research until late tonight. I've really got my back to the wall over here!
[None of the above is true, so don't worry about me!]