My view is also that the "peace" and "anti war" movement was not those things. But it was I think, not even an anti draft movement, but a socialist movement, and thus an anti American movement. It's probably true that a popular following was able to be developed simply because of a desire to avoid risking life and limb in a war about which most cared little, but the organizers were, I believe, all committed leftists, many even having been raised as communists.
The same type of people are now protesting the Iraq war, committed leftists all. Before WWII, there was also an "anti war" movement, probably also led by the Left. The national media, being leftist itself, has consistently neglected pointing out, both during the 60's and today, the socialist origins of the so called anti war organizers.
There was, and it was led by the Left, and they continued to agitate even after the war started. The Left suddenly became hawks when Hitler attacked former ally, the USSR.