One of our engineers (Kim) had a better idea which does not require you to use the Picasa client.
When you log into your Picasa web album, towards the bottom right you will see a link to 'browse by tags'. Click on the Eye-Fi tag and now you should see all pictures that are tagged Eye-Fi (which your card will do automatically). Now get the RSS feed for this 'virtual album' and use that in your digital frame.
Now any new pictures you take that the Eye-Fi card automatically uploads (and tags with Eye-Fi) to Picasa Web Albums, should appear in the digital frame.