The Washington Post contains an article on a recent survey by Oklahoma State University where over 80 percent of Americans support “mandatory labels on foods containing DNA,”
The Oklahoma State survey result is probably an example of the intersection between scientific ignorance and political ignorance, both of which are widespread.The most obvious explanation for the data is that most of these people don’t really understand what DNA is, and don’t realize that it is contained in almost all food. When they read that a strange substance called “DNA” might be included in their food, they might suspect that this is some dangerous chemical inserted by greedy corporations for their own nefarious purposes.
The article discusses the wider issue of scientific ignorance driving policy decisions, and there is some further comment at io9. A summary of the full survey results is available (PDF).
Milk has bacteria in it unless it's labeled "ultra-pasteurized [wikipedia.org]". The pasteurization process normally used in the US does not kill all of the bacteria, which is why milk will go bad even if you don't open it. Also, dead bacteria might still contain DNA, although enough heat to kill the bacteria may also include destroying the DNA.