Of course, there are many other factors that contributed to Vietnam, but such a simplistic argument that drafts prevent or cause wars is similar to the equally logically fallacious argument used by people who wish to instate the peacetime draft.
Freedom from national compulsion, including compulsion to serve was one of the reasons our nation was founded. One of the causes of the war of 1812 was the forced conscription or impressment of American seamen into the British army -- but the British were not above impressing their own citizens, when needed, into military service, something the Americans abhorred. "The Napoleonic Wars increased English need for sea power and led to the impressment of a large number of deserters, criminals, and British subjects who had become naturalized Americans" ("Impressment," Columbia Encyclopedia, 2008). America was resistant to a professional federal force in general (hence the need for the amendments allowing semi-or nonprofessional state militias the right to bear arms and preventing the forced quartering of servicemen) because of the anger the British military abuses of freedom had aroused in the colonies. During the Civil War, when New York failed to meet its recruitment quotas, making it "subject to provisions of the Enrollment and Conscription Act passed by Congress on March 3, 1863," meaning "conscription was to be employed when enrollment targets were not met by a community," New York City rioted for three days straight in an "orgy of violence" ("1863 Draft Riots," Mr. Lincoln and New York, 2002).
Thus, a peacetime draft is not a part of a long tradition of America. Freedom to choose to serve, unless historical circumstances necessitate a mandatory draft, is part of the American tradition. A professional highly-trained army accustomed to the sophisticated technological equipment in use today, rather than individuals who serve for a paltry two years is likely to offer far more effective resistance to any threat. Democratic nations that do deploy an effective universal draft, like Israel, are, in the case of Israel, nations that are involved in what might be called an constant state of tensions or war with neighbors -- and fortunately the size of Israel relative to its enemies and its need to constantly be vigilant against military invasion is not, for all of the concern about terrorism, the current state of affairs in the contemporary United States.
The arguments raised in favor of the draft are largely moral -- that all young Americans should serve, or they should be drafted deter politicians from going to war. Not electing politicians that propel the nation into war seems like a better solution than electing politicians who advocate a draft that simply 'feels good' for politicians to instate, to vaguely promote citizenship and equality, an equality of service that has never been characteristic of the draft. At present, it is true that morale is flagging in Iraq, and the forces currently deployed there are beset with difficulties. But for those who wish to pull out of Iraq, surely the best thing to do would be to deprive the military of hordes of unwilling young people, forced to fight for an increasingly unpopular cause, rather than to replenish the depleted force? If our nation requires more young people to defend its national security, then a short enforced draft might be required, but national service as a regular requirement will not act as a deterrent to war, as shown by our recent past history, nor is it keeping with the American tradition of liberty and freedom of choice. Furthermore the poorest are always likely to serve in greater number -- a new draft would likely only result in a stronger national guard, and reams of 'doctors notices' for why the most privileged were unable to serve.
1863 Draft Riots." Mr. Lincoln and New York. Lincoln Institute. 2002. http://www.mrlincolnandnewyork.org/inside.asp?ID=91&subjectID=4
Background of Selective Service." About.com: U.S. Military History. http://usmilitary.about.com/od/deploymentsconflicts/l/bldrafthistory.htm
Impressment." The Columbia Encyclopedia. 6th Edition. 27 Apr 2008. http://www.encyclopedia.com/doc/1E1-impressm.html
Vennochi, Joan. "A military draft might awaken us.' The Boston Globe. June 22, 2006. http://www.boston.com/news/globe/editorial_opinion/oped/articles/2006/06/22/a_military_draft_might_awaken_us