The SavePublishing bookmarklet could be your savior.
While viewing an article simply click the bookmarklet. It does some magic and highlights a few phrases from the article. You click on the one you want, and it pops up a Twitter dialog all set up to make the tweet happen.
Their privacy statement is interesting:
SavePublishing does not: Know who you are, or what your Twitter account handle is. It uses no cookies. We may track usage, but we'll never track you.Source: http://www.savepublishing.com/