Vincent Lafforgue's work implies the existence of the "automorphic-to-Galois" direction of the Langlands correspondence for reductive groups G over a global field of positive characteristic. I will discuss a potential converse to this for Galois representations with Zariski dense image in the dual group \hat{G}. This is joint work with Gebhard Bockle, Michael Harris, and Chandrashekhar Khare.