My Minnesota tax payment was set up for automatic withdrawal from my checking account on 4/15/16. As of today, 4/19/16, it has not yet been debited.

As long as you filed timely you will not be penalized because the IRS/State did not withdraw the money by the 18th.  See this FAQ for more information and a link to contact your State's Department of Revenue: https://ttlc.intuit.com/replies/3299924

You can also contact TurboTax Customer Support to verify how you elected to pay your taxes: Contact Customer Support