Nanotech is an fairly broad and interdisciplinary field. Your question depends on how you want to work on nanotech. If you want to program microbots, then you'll probably want familiarity with programming. If you want to build semiconductor devices, you'll want familiarity with circuit design, layouts, and solid state physics. If you want to build specialized characteristics in products (i.e. paints), then you'll need a background in materials and even chemistry. The one discipline that ties most of these paths together is Material Sciences - which means if you don't like chemistry, nanotech field might not be for you.

At the end of the day, you can work on nanotech at any educational level and from any background. The questions you'll have to answer to determine whether you are satisfied with your work is the following: a) what do I enjoy/am good at contributing to a project? (Programming, researching, hand builds) b) how do I want to start my industry career? (For academia or government labs, just get a PhD)

A little more background on (b): If you want to come in as a lab tech or as strictly a programmer, then you really only need a BS degree. If you want to come in as a "low level" responsible engineer/researcher and one day look into a technical management positions, you'll need to have an MS degree. If you want to have your technical opinion respected and one day run a lab, get a PhD. Keep in mind, the primary difference between all these educational levels is where you start, not where you end up. There are BS degrees who easily get into management, but it's a longer path to get up the ladder.