As you may already know, W3 Total Cache and Tweetblender do not seem to get on in it's current incarnation, for whatever reason.
However, there is a solution: Upgrading TB’s version of jQuery-JSONP to the latest version fixes the issue for us. (Latest version here: http://cloud.github.com/downloads/jaubourg/jquery-jsonp/jquery.jsonp-2.3.1.min.js )
It would be great to see this upgrade put into the plugin, is there any chance we'll see this happen soon? Been a few months now since an update!
Anyone else having trouble with W3TC and Tweetblender may also wish to perform this fix themselves for the time being, but the usual warnings apply, obviously.