As the war went on, more men were drafted. However, I'd like specific figures if that's possible. Internet research has yet to yield any results, I'm trying to get a scope on how the number of draftees in Vietnam fluctuated as American involvement in the theater increased.
When the war started, the draft was broadly popular. Between 1955 and 1964, only about 10,000 men were drafted monthly. As the war increased in size, that number skyrocketed. By June 1965, 40,000 men were being drafted every month. In 1966, 400,000 men were drafted (343,000 of whom were inducted). Another 300,000 were drafted annually in 1967, 1968, and 1969. The draft supported a much larger military; in mid-1965 there were about 2.5 million men in the U.S. military, and 3.5 million in 1968.
Not only were these numbers high, but deferments became more difficult to obtain. Soon, men with minor criminal records, men over 26, and married men became eligible for the draft. The unpopularity of the war, the demands of the draft, the sheer numbers involved: all took a toll on morale and willingness to cooperate. 3 draftees per 1,000 appealed in 1945. 47 per 1,000 appealed in 1953, during the Korean War. In 1969, there were 98 appeals per 1,000 draftees. Further, draft law violation went from 4 percent of registrations in 1966 to 12.5 percent in 1970. The draft was under attack from the right as well as the left: Republican leaders seized on draft reform as a way to chip at LBJ's coalition without seeming disloyal at a time of war.
Minorities were overrepresented in the draft and especially in combat units. In 1965, while African Americans made up about 10 percent of the military, fully a quarter of the U.S. soldiers killed in Vietnam were black. The military worked hard as the war continued to maintain ethnic balance; by the war's end, black casualties were only 12 percent of the total, much more in line with black numbers in the military and the general population. This could not erase the early perception that the war was a grave injustice to the black community, which contributed heavily to the riots of 1968.
The draft became increasingly divisive, until it was abolished in 1972. The last draftee was inducted on June 30, 1973.
Overall: 648,500 draftees served in Vietnam, 25 percent of the total force sent there. Draftees, because they were sent where they were most needed, accounted for a higher percentage of the dead (30.4 percent). They were a minority of the 1.7 million men drafted into the military during the Vietnam War.
Sources: Vietnam Veterans Foundation, George Flynn's Conscription and Democracy, Spencer Tucker's Encyclopedia of the Vietnam War