Generally, the funds are withdrawn by the IRS (or state) on the payment date you specified if your return has been accepted and they have begun processing it. Sometimes it may take a couple more days on their end. And if that date happens to fall on a weekend or federal holiday, the funds are typically withdrawn the next business day.
If you wish to cancel the auto-debit that you have setup and pay now, you will need to call
IRS e-file Payment Services at 1-888-353-4537 if this is for
federal tax due. Or you will
contact your state tax agency if it's a
state tax due. That way, you do not pay twice.
Otherwise, keep an eye on your bank account – if you still don't see the debit 7-10 days after your return has been accepted and they state they are processing it on their website, contact them. All processing of returns, refunds and tax payments are handled by the state and/or IRS only, after they have accepted your return.