I have now changed this widget to a new improved version. Please check out this post instead for details of the new widget, which is much easier to use and customize than the one discussed in the remainder of this post.
Since the scripts would not function using my default Blogger feeds, I decided to burn the atom.xml feed through FeedBurner, convert this to RSS 2.0 format, and express only as a summary of the posts. This way, I could ensure the feeds would display properly within the widget, and also that there is no interference to subscribers of my main blog feeds!
For a small donation towards my hosting costs, I would be willing to create a custom headlines widget and host the external files myself. Please send me an email if you would like me to do this for you.
In the near future, I will be able to offer a free service to provide static headlines widgets which you can create and customize yourselves (see this post for more details), so be sure to check back for updates soon!