A new patch for the Drupal Twitter module is available. It belongs to the feature request 793458.
The diff solves the problem when your Drupal editing address differs from the viewing url. The most common case is that you log in securely through https, but want your visitors to go to the http-version.
A more complex scenario comes up when your ssl certificate belongs to a special domain and is bound to a uncommon port, e.g. https://secured-editing.example-blog.com:8443. When you publish your new post, it then is available under http://www.example-blog.com. The tweet should contain the later address. This can be configured with the additional settings.