There are methods to analyze small samples (number of responses) from different kinds of surveys. After all, that is what the large polling organizations (Gallup, Harris, Nielsen & etc.) do for a living. The drawback of having a small sample size is that your confidence interval (uncertainty) is larger than what is normally seen in an industrial environment.
The only applicable reference I have on my desk right now is Handbook of Statistical Methods for Engineers and Scientists (Harrison M. Wadsworth, 1990.) In particular, see chapter 9, "Survey Sampling Methods."
Other useful references for the type of methods you need would be those that deal with statistical analyses in medical research or the social sciences, or other fields where small samples are the norm. In an ISO 9000 context, there are several publications on measuring customer satisfaction that may have useful methods.