In Arduino 1.8.5 and a iMac with OS X 10.11.6, Serial monitor does not show any data out of the DUE Native USB port.
I am using working code flashed from a different Mac (it is working, I don't want to risk a broken download), and I know the code and USB port are working (I can use unix commands to elicit responses and capture output out of the DUE). I've tried with and without an intervening USB hub.
Among my many tries during a couple of days it worked only once, briefly, and then stopped working during that same session.
I don't see any forum topic with this specific problem, all of them deal with either Mac USB port problems, Arduino code problems, or USB cables. But not specifically with serial monitor refusing to work when everything around it seems to be fully functional.