Connecting Google Alerts to Twitter Tweets?

I'm sure I've read on here of a way of automatically having Google Alerts connected to Tweets so your tweets are always up to date and more importantly, automatic.

Now is there software, scripts that can do this, or is a blog needed as an inbetween, where the blog posts the story and at the same time posts a summary title + link as a tweet?

TwitterGadget is all I can think of right now that might be close to what you need: http://www.twittergadget.com

Otherwise just get an RSS Feed URL to your GMail (or mail client) inbox then use a popular Feed Reader capable of posting to Twitter, ie: http://feedly.com

It's necessarily automatic, but it's as close to it as I can think. Good luck!