This is a more complex issue than meets the eye. Let's look at a few salient factors, historically and presently, to see why public policy should or should not reflect the opinion of the voters.
First, the United States Constitution has provided us with a representative democracy that includes a legislature that creates our federal laws and an executive branch that appoints our Supreme Court Justices, charged with the interpretation of those laws. When all of this began, in both instances, we were electing representatives who would create legislation on our behalf and electing presidents who would determine who would serve to interpret legislation on our behalf, in an era that included no opinion polls, no 24/7 news cycle, no internet communication, and just snailmail delivered by horses. Hence, it was contemplated that we would elect people who would exercise their best judgement on behalf of all constituents, to create legislation, to appoint good justices, or to otherwise effectuate policy for the good of all, mostly without much information on what the majority of any particular constituencies actually wanted. In short, we elected representatives, not puppets. Had it been contemplated that all public policy represent the "will" of the people, all legislation and/or interpretation could have been accomplished by referendum. Moreover, because each state is given two senators and a larger number of representatives based on the number of districts in each state, what public opinions were meant to control? Senators, at least theoretically, were meant to represent the constituencies of their entire states, while representatives had a much smaller public opinion base to consider for their districts. If all of these congressmen had been able to ascertain public opinion and had relied solely on that opinion, we would have had gridlock far sooner than we did.
Fast forward to today. Now that we do have the capability of ascertaining public opinion fairly accurately, should public policy be made in this way? What happens if polling indicates that 50% of one's constituency has one opinion and 50% has another opinion? What if there is something morally or ethically wrong with the majority's view? Should a public representative go along with that opinion? What if the representative has considerably more information on a matter, which at least theoretically should be the case? What about the democratic notion that the minority must be protected if the prevailing of the majority sacrifices rights held to be important in a democracy? Should appointments to the Supreme Court be a popularity contest? How many people would be able to intelligently make that choice?
The design of a representative democracy does not necessarily contemplate that representatives will always fashion public policy in accordance with public opinion. It contemplates that representatives are voted in and/or appointed to represent all the people to the best of their abilities, exercising their reason, intelligence, and judgement as best they can.
There are two ways to understand this question. I will give a brief answer to each understanding.
First, we can ask why it is appropriate for public policy to follow public opinion. In other words, why is it the right thing for this to happen? In this case, the answer is because that is the most democratic way for things to be. In a democracy, the people are supposed to be sovereign. The government is supposed to do what the people want. If public policy does not follow public opinion, then the people’s will is not being heard. That means that the system will not be democratic.
Second, we can ask why it is likely that government officials will follow public opinion when formulating public policy. In other words, we are asking why it is in the best interests of the officials to follow public opinion. In this case, the answer is that policy should follow public opinion to keep the people happy. This is particularly important in a democracy. In a democracy, the public officials only get to be in office if the people vote them in. If the officials consistently create policies that are at odds with public opinion, the people will be unlikely to reelect them. Therefore, it is in the best interests of the government officials to follow public opinion when creating public policy.