There is no such thing as Delta anymore, there is only Visa Debit, Visa Electron and Maestro (and wikipedia tells me there is going to a Mastercard debit launched next year).
This doesn"t help with the immediate question, but I did point this out previously yet the payment processor is still persisting with incorrect terminology.
Logically the Visa Delta option should be the one that Visa Debit works on but that doesn"t mean that it will work.