I've also got this problem, using Arduino 1.5.6.r2 trying to use the wire library with a Due board
I get the
C:\Users\xxxx\Documents\Arduino\libraries\Wire\utility\twi.c:25: fatal error: avr/io.h: No such file or directory
error.
Yet, other people have reported that they can use the wire i2c protocol with a due board. I have noticed that those who resolved the problem were using Ubuntu or some flavor of linux i'm Windows user. Currently i am running this on my laptop running Windows 7.
I need to figure it out.