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.
<div class="tweetthis" <font color='Red'>style="text-align:right;"</font>>
After removing that your text-indent:-999px works for me.
If you were trying to get your tweet anchor to the right then just float it right.
I was hoping to launch a site tomorrow,
Why are you using a transitional doctype on a new site?
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.