You don't need to put it in PHP echo statements. That should work, just a little extra unnecessary code.
Try the following:
<li class="hits">
TEST{JFBCLike layout=button_count show_send_button=false}TEST
</li>
<li>BLAH BLAH</li>Then, see if the TEST TEST and/or BLAH BLAH show. If the Like button doesn't show, but that text does, then it's an indicator of something strange going on. If nothing shows, then the template override may not be working at all, and you'll need to know where the code should really be edited. If the Like button magically appears, obviously deleted the extra stuff I added.
Finally, always make sure you're cleaning your Joomla cache after every change and try to disable any 'optimization' plugins you may have enabled.
Hope that helps,
Alex