I found an Atmel document that says that the microprocessor for the Due is capable of converting up to 1 million samples per second (ksps).
I found this statement in the ADC application note for the SAM3 processor.
http://www.atmel.com/Images/Atmel-42298-SAM3-4S-4C-Analog-to-digital-Converter-ADC_ApplicationNote_AT06860.pdf
The Due product description lists the Atmel SAM3X8E ARM Cortex-M3 CPU.
Does 1 million ADC conversion per second seem reasonable for the Due?