Any public opinion poll is only as reliable as the intellectual honesty of the people conducting the poll. You have a political science background then you know JUST how much impact HOW a question is asked has on outcomes. Start with a false premise in your question, get a false response. IF you actually dig into most current public opinion polls and look at the sample weighting, questions asked, times polled etc, you see clearly how public opinion polling is now conducted to validate and propagandize not to sample opinions.
Basing public policy on opinion polls is the behavior of fools. That is one of the reasons WHY we are a Constitutional Republic NOT a Direct Democracy. How you feel as a citizen about this or that is, an always should be, irrelevant to political leaders. We elect them to represent us, not do our bidding.
Expecting politicians to decide what to do by taking a poll would be as stupid as expecting your Surgeon to decide how to operate by asking 20 uninformed layman how to cut you. One of the fundamental problems with Modern US Political is we no longer have any leaders, we have a bunch of poll watching whores. The ONLY thing a poll is good for is to sample how well you are getting your message out, it has never been, and should never be, the criteria for making political decisions. Here is something you poll watchers should consider. Bill Clinton did NOTHING unless the polls told him to. How much did he get done? Funny thing about old Bill. Left office with approval numbers in the 60s and a likability rating of 31%. Got nothing done, left the country in the mess but was popular. If that what you think we should be seeking in a political leader, you are a fool.