The debit card is not a debit card so much as it is a check card. When you make a purchase using it, it takes a couple of days to clear, just like a check. If Target tries to get their money (like they would a regular check) and the money isn't there, boom, overdraft. So, no, the money issues are with Target for wanting their money for the original purchase and the overdraft fee and with your bank for the overdraft from them as well.