This history of the St. James Infirmary song is an interesting one. This post at Gothica Gothique tells a bit about the origins and different versions of the song.
While hanging around a folk music bar in Scotland, I found it interesting that there of all places, someone to whom I showed the early lyrics for the song was able to identify that St. James Infirmary has a common musical ancestry to The Streets of Laredo.
Something in the lyrics that is lost on many modern listeners is the implication that the "baby" of the St. James singer, who is dead at the infirmary, has died of syphilis or some other venereal disease. This is the reasoning behind the "chilling" sense that Sarah Vowell complained of where the narrator seems more concerned with his own funeral arrangements than longing to rejoin his dead lover -- thing is, he already KNOWS that he's next in line, hence the hurry toward "impressing his buddies with a big dumb coin". She's dead, and she gave him the same stuff that did her in.
The original St. James' Hospital song includes the lines --
"And had she but told me before she disordered me,
Had she but told me of it in time,
I might have got pills and salts of white mercury,
But now I'm cut down in the height of my prime."
-- Which explain much of the narrator's mindset.
There is an interesting article at Best of New Orleans trying to track the history of the tune, which is not so similar to the Streets of Laredo melody that is the older one. But in fact, a simple adaption into a minor key and change to a "blues beat" starts giving the hints of what happened to arrive at the known modern St. James Infirmary melody.