Like many of the posters mentioned, my understanding is that the difficulty in finding an NP position is all relative: it all depends on what specialty you want to do, and where you want to practice it.
One area that is heavily saturated with NPs these days is the San Francisco Bay Area. I can think of 5 nursing schools
with masters programs in nursing in San Francisco and Oakland. There is a PA program at Stanford, and I think an NP or PA program just up the road at Davis. All of these schools have been spitting out practitioners for years...and it's getting extremely hard to find a job. Even better: I'm told that many of the instructors at some of these institutions are only teaching because they can't find a job in their field. (Which begs the question: if they haven't been able to practice their art, how can they teach it? .... but that's a whole other can of worms.)
Anyhow, as for why neonatal NPs are in demand, it's my understanding that it just takes a special kind of person to handle all the emotional weight of the NICU. You have the most fragile of patients, and the most demanding and emotional of patient families. And I imagine it takes a lot of work to keep the emotional aspects of the work from interfering with your job and the rest of your life.
All of the above is, of course, just conjecture and opinion, based on my limited observations of the profession (I'm not in it...yet). But I think it's fairly accurate.
Karen: just out of curiosity, does "being in demand" translate into being paid a livable salary? My husband and I have been toying with the idea of living in Europe for a couple of years, and while I figured I could always work as an RN, it would be GREAT if there were work for a family NP.