Why am I getting "fatal error: SoftwareSerial.h: No such file or directory"
According to your comment:


  after commenting out those ifdef guards, it worked


I would say that is a bug in the Adafruit_GPS library.

As a matter of fact, the DUE is not using the AVR architecture (it uses ARM), that explains why #ifdef __AVR__ in Adafruit_GPS.h never passes; but then something else should be done specifically for the DUE (missing #else or #elif).

After checking on github, there is an issue open for that; unfortunately, as of April 2014, it has not moved for 10 months.

Your best guess would be to go there and try to "reactivate" this issue.