MercyMe’s “Say I Won’t” centers on the idea of the narrator’s experiencing a new lease on life. He has become aware of a heightened potential which living holds. In the first verse, he sounds sort of like he had a life-changing event or at least an epiphany which has made him realize that he has been operating under maximum capacity.
 
And the second verse, with MercyMe being a Christian band, has him acknowledging that “the Spirit inside” is greater than the self-defeating ideas which originate externally. So, he is now dedicating himself to living life to the fullest. And the title reads as if he is daring those who believe that he “won’t” achieve this goal.