After many hours with ESRI Tech Support we figured out what the problem was. I had added the "PYTHONPATH" system environment variable at some point and this confused the ArcCatalog Publishing Task so that it could not find Python. This basically sends the Publishing Task into an endless loop and you don't know what is going on and nothing is happening. For some reason you cannot publish scripts that import the os library. Scripts without that still publish.
In short, DO NOT add a "PYTHONPATH" system environment variable!
Why did I do it? I think I've been adding that variable for years. It was recommended to me at some point for using Python at the command line. Doh!
Thanks, Dave