Category ID returns as ‘0’?

Question

Answered my own question, although not exactly how I had originally intended.

    <?php 
        $cat_name = get_theme_mod( 'cat_1' );
        $cat_name = str_replace(' ','-',$cat_name);
    ?>
    <?php query_posts('category_name=" . $cat_name); ?>

So instead of trying to convert the category name to the category id, this seems to convert the category name to the category slug.
I can test this by echoing $cat_name and it returns the category slug and not the category name.

In any case, this works now. Posted so others can use it if they need it.