In my opinion he is just saber rattling to avoid camp and to get the attention that he so desperately seeks all the time. I could be wrong, but I would imagine that he will be behind Center for Green Bay when the regular season starts. With or without a new contract.
Both parties have no real leverage, which is weird but true. If the Packers let Rodgers leave or make him sit out by playing hardball, then here comes a 6-10 season at best. On the other hand, Rodgers really can't be traded right now for many reasons so his only real options are to sit out the maximum number of games that would still let your contract toll or retire.
At the end of the day, I think they come to an agreement that this is his last year in Green Bay and he doesn't get any fines for sitting out. You are right, Rodgers loves attention but he is very stubborn and I can't rule out the possibility he retires out of spite. He has a ring, his money and a ticket to Canton. I'm sure he wants to keep going but he wouldn't be leaving with regrets.