Wheeler earned a Bachelor of Arts degree from the University of Texas in 1950, and a law degree from University of Texas School of Law in 1954. Upon graduation, Wheeler ran for election in the Texas House of Representatives, and served three consecutive terms—from 1955 to 1961—as a Democrat representing the 69th District. Tilden chaired the Public Lands and Buildings committee, and was vice-chair of the Liquor Regulation committee. During his tenure, Wheeler also assisted with his father's ranching business in Tilden.
