The state will pull the funds, not TurboTax. Generally, the funds are withdrawn on the payment date you specify if your return has already been accepted but can take a few additional days. If you still don't see the debit 7-10 days after your return has been accepted, you will need to contact your state tax agency, if you owe a state payment. 

You can choose your state below and it will take you to their contact page with phone numbers to reach them. 

https://ttlc.intuit.com/replies/3302452