Programming jobs are not unlimited. There's just a big demand for programmers and lack of supply. If every wannabe musician/artist/celebrity wanted to be a coder we'd certainly feel the strain.
marshallp has a point. There is a limit to the demand for food; after a while, you are full. There is no hard limit to the demand for technology, because the value that technology adds is the ingenious solving of problems, and it seems that everyone always has problems.
Programming is fundamentally different to any other activity because it operates at a meta-level, it's about the automation of work. As long as there are people working, programming hasn't reached it's saturation point.