Adding BG Color To #menu ul li

I’m trying to modify the following stylesheet:
http://www.alexking.org/software/wordpress/styles/sample.php?wpstyle=blorange
I would like to add a background to the side menu list items and I want the background color to span the entire width of the side bar. Simply modifying #menu ul li isn’t enough but can someone suggest how I can make additional changes to get the result I want? I would like to include the links also so I would have to change some PHP for that since changing wp-layout would background color the entire list. I kind of imagine that someone has already wanted to do the same but several pages into a search yields nothing exactly like this.
I did a span style in the index.php for demo purposes so that it would render similarly to how I would like it:
http://www.thedesignofitall.com/index.php
Thanks