In 1983, Dodge was named the starter for the opening game, but a shoulder injury in the final preseason scrimmage on Sep 9, sidelined him for a month and he didn't reclaim the starting role until early November. In late October he twice came in off the bench to replace starter Rob Moerschell and rally the Longhorns to wins. He came in late to throw the go-ahead touchdown pass in the 15-12 win over SMU, and early the following week to lead the Longhorns to a 20-3 win over Texas Tech. The next week he got his first start of the season in a 9-3 lackluster win over Houston. But after struggling in the TCU game the next week and being replaced by Moerschell, he didn't play the remainder of the year. Despite the quarterback troubles that resulted in rotating starters, the Longhorns went undefeated during the regular season and, but for a disappointing loss to Georgia in the Cotton Bowl, would have won the national championship.