The problem with a poll is that the general public is likely not privy to all the information that the people in charge have. I think the best thing to do here is just come out with all of it, lay it on the table, and see what the public thinks then. If you have a good reason then show us.
That is exactly what the government has not done all these years. Why be tight-lipped if there is solid evidence and data, its not some issue of nuclear weapons/military-strategy.