While in law school in the late 1960s, an era of escalation in the Vietnam War, Burke received a draft deferment as a full-time student. After his marriage and the death of his father, he applied for and was granted a hardship deferment (3-A), as the sole support of his wife, mother, and two younger brothers. In June 1969, the Illinois Selective Service board of appeals reclassified him 1-A ("available for unrestricted military service"). At the same time, he was accepted into a Chicago-based United States Army Reserve unit, the 363rd civil affairs group, as a private. Political rivals expressed concern that special consideration allowed Burke to join the Reserve unit ahead of others, but an Army investigation found no evidence of manipulation in his favor.