Hello eriknyquist,
I got one SAM-ICE JTAG directly from Atmel for debugging Due (after Atmel tech. support recommendation).
http://store.atmel.com/PartDetail.aspx?q=p:10500253#tc:description
I haven't used recently but I debugged a couple of sample projects in my Due with Atmel Studio 6 IDE, and it worked OK. I also ran the diagnostics tools J-Flash ARM v4.56d and J-Link ARM v4.56, and also ran OK. I even made debugging tests on my SAM3X-EK and no problem. The only problem is that SAMICE is very expensive (~$100) and you will need the cable ARM-JTAG-20-10 (~$7) for the 0.05" connector.
If you are lucky, you can buy one cheaper on Ebay. If you are a developer, it worth the price.
I think is good for you to know that SAM3X8E (Due) doesn't have instruction trace capability (I mean, it doesn't handle the debugging instruction trace module: Embedded Trace Macrocell (ETM) available in its Cortex-M3 core, but it does fully support all other ARM CoreSight features through Serial Wire Viewer.
There is a second option: J-Link by Segger. It costs a bit less (~$63).
Regarding Massimo's solution, I don't know but it seems to be less expensive. Good luck!