If you’re into a bit of constructive tweaking of Blogger you can get it to generate an RSS/XML feed. But you need to be using Blogger to publish to your own site. Here’s the link” hit-or-miss.org: How to manage your site with Blogger, PHP, and XML
I see also that Blogger has just announced support for Atom to handle syndication. Check out: Syndication. It’s not RSS but some of the RSS aggregators support it.