Arduino Due Incompatibility

[alexceltare2]

Hello, I would like to start by posting my first problem on this forum.
I've been working with Arduino Uno and Due for a while and noticed something irritating. After the ESP8266EX module came, i've updated the firmware to the latest 0.9.6 using Arduino Uno and worked nicely with that board, but when I try to connect it with Arduino Due, I send AT commands and whatever I can but no response/output comes up. I've already tested with all Baud rates(on Arduino Uno it responds to 115200bps and before fw update to 9600bps) and 3.3V and 5V pins but nothing seems to come up. The Blue LED blinks meaning it transmits commands but nothing so far. My theory was that the current needs to be about 300-400mA peak and Due doesn't seem to cope with that much.
So my question is: Is it possible to launch a new firmware to work with lower current sources?
Thank you for your time