TurboTax gets no information about your federal or state tax return after it has been filed and accepted. Did you confirm that your efiled state return was accepted? https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp
If it was accepted, then it is up to the state to debit your account based on the instructions you included on your state tax return. Did you confirm that the routing number and account number that you entered on your state return are correct?
If the state has not yet totally processed your tax return, they may not have issued any instructions to debit your account yet. You can contact your state to get the status using this link: http://turbotax.intuit.com/support/kb/state-taxes/state-issues/1274.html
