Can those of you having trouble here confirm whether any of your blogs are set to private? In looking at the importer code, I've noticed that a couple of the blogs seem to require me to log in to view them. When I set one of my test blogs to be viewable only by myself, I can reproduce the error you're encountering. And given the nature of the error, a private blog would seem to be a reasonable cause.
I've tweaked the importer page to handle private blogs more gracefully. Instead of showing a simple error message, you should still see the import page now, with a warning about the blog(s) causing the issue. To import any of these blogs, you'll need either to set it to be publicly viewable during the import or to fetch the export file from Blogger, available under the blog's Settings page (a tiny "Export blog" link near the top of the page).
If you opt to turn privacy off during the import, you'll need to use the "reset importer" button on our import page after changing the privacy setting. You should then be able to import.
I'd be grateful for confirmation that this resolves the issue, or of course for further error reports.