Depends on what you mean by “Mexican” and what you mean by “holiday”. “Mexican” comes from “Mexica” which is the name of the dominant Aztec tribe at the time of the arrival of Cortes. read more
For Mexican national holidays (Independence and Revolution days), there is a greeting which is not really polite or proper, but very popular nevertheless and goes like "Viva México, cab***es!" ("Long live Mexico, *$$holes!"). read more