As a fan until your eliminated, you want the team to win to build on. Granted in this case in may be mitigated by the possibility that 1/2 the team will be leaving.
After that, I rather take a long range view incl better draft choice, easier next year schedule etc, than win a few meaningless games.
Unless there is somebody out there that you think is a vast improvement, A BB, Parcells, Jimmy Johnson, Vermiel, Walsh type, you let Rex drive next year.
As far as the front office goes, that is something else. I would not want them to draft some 3-4 lbs and then have a new coach come in next year (2014) and want to run a 4-3.