If I set up a auto debit from my checking account for the state taxes how long should it take to be withdrawn? How do I look to see if it is in fact to be auto debited?

You can verify if you have scheduled step-by-step payments and the dates by accessing a copy of your tax return.  
How do I get a copy of a return I filed this year in TurboTax Online? 

If you chose to have them withdrawn from your bank account, generally, the funds are withdrawn on the payment date you specified if your return has been accepted. If you still don't see the debit 7-10 days after your return has been accepted and your specified date, you will need to call your state to inquire.