Cika wannan jumla:
A taron kasa na jam'iyyar Democrat na shekarar 1956 a Chicago, tsohon Shugaba Truman ya goyi bayan Gwamna Harriman, ga takaicin Stevenson, amma tsohon mataimakin shugaban kasa Eleanor Roosevelt ya ci gaba da goyon baya. Stevenson ya ci nasara da sauƙi a kan Harriman a kuri'ar farko, ya lashe zabensa na biyu na shugaban kasa na Democrat. An taimaka masa da goyon baya mai ƙarfi daga wakilai matasa, waɗanda aka ce su ne ainihin ƙungiyar "New Politics". A kokarin da yake yi na kara himma ga tikitin jam'iyyar Democrat, Stevenson ya yanke shawarar da ba a saba yi ba na barin zabar abokin takararsa ga wakilan taron. Wannan ya haifar da gagarumar gwagwarmaya tsakanin manyan 'yan Democrat da dama don lashe takarar mataimakin shugaban kasa, ciki har da Kefauver, Sanata Hubert Humphrey, da Sanata John F. Kennedy. Bayan ya kawar da kalubale mai ban mamaki daga Kennedy, Kefauver ya lashe zaben mataimakin shugaban kasa a zagaye na biyu. A cikin jawabinsa na karɓar, Stevenson ya yi magana game da shirinsa na "New America", wanda ya haɗa da fadada shirye-shiryen New Deal zuwa "yanayin ilimi, kiwon lafiya, da talauci". Ya kuma soki 'yan Republican saboda kokarin "sayar da' yan takara kamar hatsi na karin kumallo".