Jung joined the SA in 1927 and the Nazi party in 1930. In 1933, after the Nazi Machtergreifung, he became president of the Hessian parliament. After the dismissal of Wilhelm Ehrhard by the Nazis, Jung was appointed provisional mayor of the city of Mainz. Already in Mai 1933 he was displaced by Robert Barth. He was prime minister of the People's State of Hesse from September 1933 until March 1935 when this function was taken over by Jakob Sprenger. During World War II Jung was the mayor of Vienna (1940–1943).