Minimum Sample Size for a Survey

Hi guys,

Here's a question I've been struggling with over the past week. My employer would like to perform a survey to gauge public opinion on a number of government agencies. I'm trying to put together the concept and one of the questions I've run across has been "what would be the minimum sample size necessary for each agency?" I realize it depends on variability and the degree of confidence desired, but can't seem to pull together an answer.

Let's say I'd like the largest commonly acceptable margin of error (5%? 10%?). Would it be OK to aim for only ~20 respondents per agency? I'm already focused on the demographics and all, but just can't figure out the quantity I'd need.

Thanks a lot,
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The outcome would be a score or rating, to keep it simple.

A little more detail -- the rating would be a composite score based on the respondent's answers to twenty or so questions across five dimensions, according to the framework we've defined.