Depending on where you want to start, there are plenty of places to find opposition. George Kennan detailed the flaws in fighting such a war in his "containment policy." I believe it is titled Article X. One of the most vocal groups was the SDS (Students for a Democratic Society). They were bothered by Cold War policy--the threat of nuclear war, unrest abroad, etc. They felt more energy should have been focused on domestic issues like the was on poverty and civil rights. Dr. King also spoke out against the war. Others felt the draft was unfair as well.