Universal National Service Act - Declares that it is the obligation of every U.S. citizen, and every other person residing in the United States, between the ages of 18 and 25 to perform a 2-year period of national service, unless exempted, either through military service or through civilian service in a federal, state, or local government program or with a community-based agency or entity engaged in meeting human, educational, environmental, or public safety needs. Requires induction into national service by the President. Allows persons to be inducted only: (1) under a declaration of war or national emergency, or (2) when members of the Armed Forces are engaged in a contingency operation. Requires each person, before induction, to be examined physically and mentally for classification for fitness to perform. Sets forth provisions governing: (1) induction deferments, postponements, and exemptions, including exemption of a conscientious objector from combatant training and military service; and (2) discharge following national service.