They absolutely do. On September 12, 2001, ~nobody in the United States was interested in starting a war with Iraq.

Two years of propaganda later, and all of a sudden, half the population had acquired keen geopolitical insights which necessitated an invasion and occupation of a country that had exactly fuck-all to do with 9/11.

A decade later, all of a sudden, nobody wanted to fess up to wanting anything to do with that mess.

Public wants aren't discovered in some interference-free democratic vacuum. The people who own the press put a millstone on their side of the scales.