He will have a bad game at some point because all QBs have bad games; it won't be some kind of deep psychodrama between him and Romo playing out.
If anything, Dak has seen how quickly the Cowboys fanbase turned on Romo, and knows they'll do the same thing to him in a heartbeat. Romo has to be one of the best players hated by his own fanbase, and Dak has to know he's next in line for the same treatment the second he loses a game, or God forbid is the holder on a field goal attempt that goes wrong.