The first thing I would do is get rid of all the inline css text-align styles in your tweet this divs. Mainly because there is no reason to mix markup with presentation. Secondly because it appears to be part of the problem.
After removing that your text-indent:-999px works for me.
<div class="tweetthis" style="text-align:right;">
If you were trying to get your tweet anchor to the right then just float it right.
Why are you using a transitional doctype on a new site?
I was hoping to launch a site tomorrow,
There is no good reason for it, use a strict doctype and keep the inline styles out of there.
^I see, it's a WP theme. I suppose that is how the tranny DT got in there.