There are a number of questions, issues and problems associated with mandatory government service for 18 to 21 year olds. To be sure, the United States government has mandated government service in the past for young Americans in the form of the draft. However, the draft was the result of a crisis -- specifically war. The all volunteer U.S. military does not necessarily favor the draft because the caliber of recruits it would receive would likely be lower than the type of person the U.S. military is currently accepting into its all volunteer ranks.
People in favor of re-instituting the draft may have a specific political agenda in mind. Specifically, the war in Iraq. It is easier to accept the fact that Americans are dying every day in "post-war" Iraq because we know that they military personnel assigned to the region joined the U.S. military voluntarily. If young Americans were drafted into the U.S. military for mandatory service to the country and ended up in the line of fire, it is reasonable to assume that support among American people for this intervention would drop rapidly.
Of course, not all mandatory service for 18 to 21 year olds needs to be in the U.S. military. Young Americans could be put to work on community projects as well as in local hospitals and schools. On the surface, this idea seems more palatable than sending young people off to war. The question that must be answered is this: In the absence of a compelling reason to mandate government service for able bodied Americans aged 18 to 21, would requiring or mandating such service be Constitutional.
I would argue that mandatory government service in the absence of compelling national emergency, such as a war, would be unconstitutional. Among other provisions of the Constitution, that such a program would violate would be individual freedoms, and the right to "life, liberty and the pursuit of happiness." Mandatory government service might also...