There are a lot of people who do it, so its clearly possible. But, as with anything, the larger question is whether its possible to make a living at it and still maintain your passion for it and still love it? This is much much harder and much rarer out in the world. I know a number of wedding photographers who make a living but don't really enjoy it much - its just a job now... There are probably some photo-journalists who still love it. But I don't think there are many street or landscape photographers out there making a living and loving it. Maybe a few from the big magazines, but its pretty rare.
Then again, the question reminds me of the old joke, "If you want to end up with a million dollars as a photographer, start with two million"! This is often applied to bike shops, jazz clubs, other jobs that people go into with a lot of passion and come out of exhausted and broke...
-Ray