You could use CSS Table display layout to distribute your nav items. Its well supported across browsers and simple to implement:
.navbar-nav {
display:table;
width:100%;
margin: 0;
}
.navbar-nav > li {
float:none;
display:table-cell;
text-align:center;
}
This makes it 100% the width of its parent #header
, which in turn is restricted by the width of #page
, so if you need it to span 100% of the whole document width you'll need to move it out of #page
or make #page
wider.