I had a few extra minutes so I thought I'd try and see what's up with Blogger and Picasa. Seems that with the "new" Blogger it does work. If you are not able to make it work, try 1) downloading the latest version of Picasa and 2) logging into Blogger and "upgrading" your account to the "new" Blogger (this will require that you have a Google account if you don't already). The posting process seems a little different, but pretty straight-forward.
Side note: by default it seems to post the entries as "draft" which means to have to then log into Blogger, go to the entries, and make sure that you publish the draft entry that should be there.