The "btn-group btn-group-justified" does not break down for mobile. What you're looking for is the justified navigation set up demonstrated here:
http://getbootstrap.com/examples/justified-nav/
<ul class="nav nav-justified">
<li class="active"><a href="#">Home</a></li>
<li><a href="#">Projects</a></li>
<li><a href="#">Services</a></li>
<li><a href="#">Downloads</a></li>
<li><a href="#">About</a></li>
<li><a href="#">Contact</a></li>
</ul>
It might be easier to roll your own since over-riding the nav nav-justified might be too much. Here's something: http://jsbin.com/ehaRIQA/1/edit & http://jsbin.com/ehaRIQA/1/