Dodge played quarterback at Thomas Jefferson High School in Port Arthur, Texas, under coach Ronnie Thompson where he set several state records. As a senior in 1980, Dodge set the record for most passing yards in a season and became the first quarterback in Texas high school football history to pass for more than 3,000 yards in a season (3,135 yards). That same season, he led Jefferson High to the 1980 Class 5A state championship game against Permian High School of Odessa, Texas. He also set Texas high school records for most career completions (382) and most completions in a season (221); while finishing his career with the second most career passing yards behind Gary Kubiak.