I had a few problems using libraries with the Due. I do not think the servo library is compatible by default, but there is a modified copy floating around somewhere in this forum.
I cannot find the page where these files are hosted originally, but I have attached the two files I've been using to drive servo's on my Due.
I've been placing these files in the same folder as the sketch I'm working on, then typing
#include "servo.h"
as opposed to
#include <servo.h>
This way, once you save the sketch and reopen, it will open the servo.h file in another tab, and you can be sure you're using the modified version.
Hope this helps, Phil.