There are people whose job it is to listen to audio recordings of
music performances (over and over again), and write down the notes
that were played.  They're transcribing a jazz improvization of Fats
Waller or Thelonious Monk, for example.  How many people made their
living as professional music transcribers in the USA in 2003?

Folks probably aren't making a full-time living doing this -- they're
probably doing other music-related activies in their life (e.g.,
performing, composing, arranging).  But I'm still interested in the
total number in the USA who do this
professionally (i.e., they get published and paid) at least part time.

johnq2,

 If you're talking specifically in the jazz genre, to my knowledge
none exist. 2 reasons.

 One, because of the relative simplicity of today's music, photo
copying and the development of ear training as an extension to
learning an instrument, transcribers are not much in demand. You'll
only find such detailed worked that is actually published/distributed,
devoted to popular rock music artists like the couple Led Zeppelin
Complete Guitar Tab books, I have.

 Two, because jazz musicians in particular tend to have the most
trained ear, surpassed only be classical players, maybe. And, they put
it to good use deconstructing recordings by the greats and their
idols. I have a notebook filled with transcribed guitar favorites, and
most jazz players I know, have the same.

 Your best bet, is to find a musician message board tailored to your
preference - their must be one out there. Developing friends there or
with good players locally, may get you closer to such troves of
material you're looking for!