I don't know many people who take opinion polling on policy issues as definitive in any way, but James Fishkin's piece in the Boston Review on polling had two interesting anecdotes on just how unreliable polling can really be:
Sometimes the "opinions" reported in polls do not exist. Because respondents do not like to say "I don't know," they often pick an answer more or less at random. When George Bishop of the University of Cincinnati asked in surveys about the "Public Affairs Act of 1975," the public offered opinions even though the act was fictional
The second problem with conventional polling is that sometimes the responses to questions do not express real opinions but simply the first thing that comes to a respondent's mind. This phenomenon was first described by the eminent political scientist Philip Converse. A National Election Studies panel was asked the same set of questions each year from 1956 to 1960. The questions included some low-salience items about such subjects as the government's role in providing electric power.
Converse noticed that some of the respondents offered answers that seemed to vary almost randomly over the course of the panel. They cared so little about the issue that they could not even remember what they had said the previous year in order to try to be consistent. Converse concluded that significant numbers of people were simply answering randomly.The Fishkin piece, by the way, advocates "deliberative polling," a process which would gather a representative group of people together on some weekend retreat or other, poll them on an issue, let them talk it out, and then poll them again to see what they think after some thought, discussion, and, well, deliberation. It's an interesting idea, but either way, the piece is a good reminder that people can say all sorts of things about various intricate policy programs, but that's no indication as to what they really might think about something if they gave it some actual thought.