Public opinion is presumptively an input to policy formation in a democracy because politicians respond to it or at least are believed to respond [to it].
When we are high and airy hundreds say
That if we hold that flight they'll leave the place,
While those same hundreds mock another day
Because we have made our art of common things.
Nihil est incertius vulgo, nihil obscurius voluntate hominum, nihil fallacius ratione tota comitiorum. (Nothing is more unpredictable than the mob, nothing more obscure than public opinion, nothing more deceptive than the whole political system.)
We were very effective, and I was very effective, in shaping public opinion around my campaigns. But there were big stretches, while governing, where even though we were doing the right thing, we weren't able to mobilize public opinion firmly enough behind us to weaken the resolve of the Republicans to stop opposing us or to cooperate with us. And there were times during my presidency where I lost the PR battle.
Public opinion, I am sorry to say, will bear a great deal of nonsense. There is scarcely any absurdity so gross, whether in religion, politics, science or manners, which it will not bear.
Happy is he who looks only into his work to know if it will succeed, never into the times or the public opinion; and who writes from the love of imparting certain thoughts and not from the necessity of sale - who writes always to the unknown friend.