I personally have not used a debit card for a rental, but I would be very cautious of doing it if the account is linked to your main source of funds. If something happens to the car, the rental company can charge your card for fines, penalties and damages, especially for smaller dollar amounts that normally wouldn't pass through insurance. You are much better off using a credit card, even a small limit one.
Most agencies that do accept debit cards often require a deposit equal to the rental plus a percentage above or a minimum of $200, which ever is more.