I was trying to do this on Drupal 7 with the " fb_likebox" module (https://drupal.org/project/fb_likebox). To get it to be responsive. Turns out I had to write my own Contrib module Variation and stripe out the width setting option. (the default height option didn't matter for me). Once I removed the width, I added the <div id="likebox-wrapper">
in the fb_likebox.tpl.php.
Here's my CSS to style it:
`#likebox-wrapper * {
width: 100% !important;
background: url('../images/block.png') repeat 0 0;
color: #fbfbfb;
-webkit-border-radius: 7px;
-moz-border-radius: 7px;
-o-border-radius: 7px;
border-radius: 7px;
border: 1px solid #DDD;}`