It sounds like there may be an issue with your login either to WordPress.com or to Facebook. Could you please try the following steps?
1. Go to Settings > Sharing in your blog's Dashboard and click on Disconnect from Facebook.
2. Reload the page and confirm that the Facebook is "Disconnected".
3. Log out of WordPress.com by going to My Account > Log Out (on the top left of every page on WordPress.com).
4. Go to Facebook and log in. Inside Facebook, click on Account > Application Settings (on the top right). Find “WordPress.com” and remove it by clicking the “X” next to it. If you can't find WordPress.com, just skip this step.
5. Log out of Facebook by going to Account > Logout (in the top right).
6. Clear your browser's cache and cookies. Note that this means that you'll be logged out of any site you're logged in to. That's an annoying side effect, but it's an important part of the debugging process. If you prefer, you can just clear any cookies with "wordpress" or "facebook" in them. See here for more information about clearing cache and cookies:
7. Log back into WordPress.com: http://wordpress.com/login/
8. Go to your Settings > Sharing and click on Connect to Facebook to restart the connection with Facebook. Follow the on-screen instructions to complete the connection.
This should be it - you can now try publishing a new post to see if Publicize works. Before publishing, make sure the Facebook checkbox is checked
Sorry for the long list of steps. Please let us know how it goes.