gcampos:
Yes, and SS pin too. (can SS be not wired?)Power from separate LM1117-33; 800mA available.
which pin did you choose for SS on Due? did you set it with WiFiSpi.init()?
there is a small problem with esp8266 SS pin. If esp is reset and the master holds the SS HIGH, then esp doesn't boot (io 15 must be LOW at boot). my recommended solution is here