A working demonstration : http://jsfiddle.net/dystroy/V97DJ/
$('.unc_path').click(function (){
var text = $(this).text();
var $input = $('<input type=text>');
$input.prop('value', text);
$input.insertAfter($(this));
$input.focus();
$input.select();
$(this).hide();
});
The idea (see comment above) is to dynamically replace the span with an input, only cross-browser way I know to have selected text.
Note that this is only half the road, as you probably want to deselect, style to remove border, etc.
And I must also precise that an input, contrary to a span, cannot span on multiple lines.
I don't think this could/should be used in a real application except in a very specific point.
EDIT : new version : http://jsfiddle.net/dystroy/A5ZEZ/
In this version the text comes back to normal when focus is lost.
$('.unc_path').click(function (){
var text = $(this).text();
var $this = $(this);
var $input = $('<input type=text>');
$input.prop('value', text);
$input.insertAfter($(this));
$input.focus();
$input.select();
$this.hide();
$input.focusout(function(){
$this.show();
$input.remove();
});
});