I\'m having a minor problem with Mixed-content on HTTPS served pages on our site, when we include the http://platform.twitter.com/widgets.js
Apparently Twitter doesn\'t
Had this same problem.
Was able to work around it by making my own javascript popup window and passing the params in manually. Doesn't depend on any external twitter stuff.
You'll have to download the tweet button image and save it locally on your own servers as well.
You can use something like this to encode the text of the tweet and url if needed: http://meyerweb.com/eric/tools/dencoder/
Here is a description of the params you can pass in to that URL: http://dev.twitter.com/pages/tweet_button#properties