When I was "draft age" in 1968, my graduating class at the University of Pennsylvania (or the 90 percent who were males) collectively felt like rats caught in a trap. The clear majority -- even at Penn's Wharton School of Business (classmates included Donald Trump, Michael Milken, Revlon heir Charles Revson, and, the Chairman of Merrill Lynch's son, Donald T. Regan, Jr.) -- were against the Vietnam War (well, maybe not THOSE guys!) and were at immediate risk as graduate school deferments were being eliminated.
In the late 1960s, we had few choices -- submit to the military draft (serve two years with no choice as to where you serve or in what branch of the military), "voluntarily" enlist in the military for at least 2-3 years, claim conscientious objector status (explanation to the younger folk among us: "C.O.s" were opposed to war and violence in general on religious or moral grounds and would not carry a weapon or be trained to use one, but would likely go to war anyway as a combat medic), seek an exemption to the Draft on health grounds (California excuses: surfers' knees or surfers' knots on the top of their feet making army boots painful to wear; sweating palms which made using a weapon difficult, bad eyesight, low I.Q and more). A whole generation of draft lawyers sprang up around this and very few of my West Los Angeles friends in fact served... like just two that I know of!
Also considered were other options like moving to Canada or Sweden as those governments provided sanctuary and gave citizenship to many thousands of young Americans. Those who went there before being inducted into the military were allowed home eventually but those who went Absent Without Leave (AWOL) and left were considered defectors for many years.... some were pardoned by various American presidents but many served federal prison terms when they returned home.
Yes, there was an active discussion of National Service, European style (e.g., many choices as to what you did but with an obligation written into law that every citizen, male and female, serve at least 18-24 months ) but once the U.S. Military Draft was replaced by the all-volunteer military in the 1970s, Americans basically went to sleep for two decades until the 1990s. AmeriCorps, under President Bill Clinton, while a U.S. Government funded program like the Peace Corps, nonetheless spawned private nonprofits like City Year, Teach For America and many others to re-brand public service as hip, career-enhancing and an early opportunity in one's life to give back.
I have trouble believing that a large majority of America's young (with their parents' support) would not serve if offered the opportunity. I think a courageous future president and a sentient U.S. Congress could craft a national referendum on National Service, which offered a range of choices, modest financial incentives (health insurance coverage, etc.) and a career boost through useful training programs... and see it pass overwhelmingly.
Richard M. Walden, 67, served in the US Army Reserves in 1968-1971, was trained as a Combat Medic although he did not serve in Vietnam. His Operation USA, an international relief agency, flew the first American post-war humanitarian aid back into Vietnam and Cambodia in 1979... and shared the 1997 Nobel Peace Prize as a member of the International Campaign to Ban Landmines.