Its not made yet, but I've got a quick little flow chart thrown together in how to make it function.
You can get widgets like
these on a site already, twitter puts them out. They also have a more or less complete API so that people can write their own applications to interact with twitter.
As it is, what the widget would be is like the widget w/ friends badge, except brandable (you can put your own logos and such on it). There would also be a login button so that you can log into this widget (on whatever site it resides) and make posts directly from twitter from it. Then, there would be some kind of setting the site owner can change which would make it so that the feed on the site would include the last X many people to tweet from their site.