A shutdown, complete with worker furloughs, will reveal to most people how unessential everything it does is for their lives.
Normalizing life without DC doing whatever DC does is an essential step to selling political dissolution to the general public. We are headed for a breakup one way or the other. A soft landing, with dissolution done in an orderly and peaceable fashion, is preferable to the crash landing that will happen after a deep economic recession and subsequent debt crisis.
How will life be different if your state peacefully separates from the union? To a first approximation, a quarter of your paycheck will no longer be taken out in taxes each week and the deposit into your account will be that much larger. You will no longer get whatever it is you received in return for that deduction. Other than that, pretty much same old, same old.