I think it would be a very minor consideration. If Jerry really thinks Jason Garrett is the man for the job, he'll retain him. Then create something to get attention involving the team--positively or negatively--that will become the offseason narrative. Some off-hand comment that indicates Garrett's been neutered. Some attention-getting statement to get people talking about how senile the owner is. Something to garner some press and some attention for the team to fill the vacuum that keeping the head coach in place would create.
The real question is 'how much does the organization really think the problem is Jason Garrett?' My guess is that they don't really think the issue is the coach, and unless the vibe is that he's losing the confidence of the team, I can readily see them sticking with him. That said, it does sound like the defensive players are starting to question the defensive scheme behind the scenes. That's usually not a good sign for any coach. I think a lot depends on the team's mindset the next two weeks, honestly. If we're still able to beat the bad teams, that will say a lot. If we're getting beat by bad teams, that says a lot, too.