Q (1999): You've said that you tend to "bury" directly autobiographical stuff. What about Who Are You? Should we know who that's about?
TW: "Gee, I dunno. I think it's better if you don't. The stories behind most songs are less interesting than the songs themselves. So you say, "Hey, this is about Jackie Kennedy." And it's, "Oh, wow." Then you say, "No, I was just kidding, it's about Nancy Reagan." It's a different song now. In fact, all my songs are about Nancy Reagan."
(Source: "Mojo interview with Tom Waits ". Mojo: Barney Hoskyns. April 1999)
Waits, like quite a lot of writers, never likes to give too much away about what his songs might mean. You could certainly read that as a song about someone who is going to commit suicide. You could possibly read it as a song about someone who is dying.
I would not agree with Joe that Waits has written lots of songs that could be considered "suicidal," but I do agree with him about the Holly Cole cover. The version on the album Temptation (which is all Waits songs) is one I like a lot