I actually did this for my blog. I had the tagline “Brickbats for Asshats since 2004” on my old BraveJournal blog and I insisted on including it on my WP blog.
I opened up header.php in my theme folder and did a little editing. I already have a class called SmallFont that I use when I want something in a small font that calls the following css:
.SmallFont {font-size: .9em;}
I made the following modification to my header.php to display the tagline:
<div class=”description”><?php bloginfo(‘description’); ?>
<em class=”SmallFont”>Brickbats for Asshats since 2004</div>
Note the line directly below where bloginfo(‘description’) is called. (I wanted to include the whole block, but WP kept mucking up the h1 line so I deleted it from this post) That’s how I insert my tagline, and it appears on every page. You can add a link with no problem.
That may do just what you’re thinking of.