I think it being the bye week, it's their one opportunity to give TVD another chance but - as you mentioned - they should have a short leash on him. B/c if they put Jake in and he doesn't play well, then what? You can't go back and forth with them. The bye week gives them the opportunity to say that they worked on some things and still believe TVD is the guy and then if he plays like crap again, you pull him.
Now if behind the scenes TVD is not showing the right attitude, Jake looks better than him in practice or it is clear that the team has given up on TVD, then yes - just go ahead and pull TVD now.
All that being said - and as someone who was never previously on the Jake should be playing ahead of TVD wagon - the attitude (or at least the perceived one from what we have seen on TV and interviews) from TVD this season does not seem like it is in a good place. Not sure if he is just super frustrated with the offense, himself or what but it doesn't give me much hope that things are going to turn around for him as long as he is here.