"Whose side are you on?" the image asks, pitting the conservative credentials of Cornyn against those of Stockman, who "Voted to defund Obamacare" and "Stands up for conservatives."
Stockman defended Robertson in an appeal to supporters posted on his campaign website Thursday.
"Whether I agree with Phil Robertson or not, it is WRONG to take away a man's job for voicing his personal religious beliefs," Stockman asked his supporters to tell A&E Networks. "I will no longer be watching A&E, Lifetime, HISTORY, H2, HISTORY en Español, Military HISTORY, HISTORY Education or BIO until Phil's suspension is lifted."