To head off what will undoubtedly be some support requests, I wanted to let you know about a change in the Twitter API as of January 14th, 2014.
The Twitter API used to accept either HTTP or HTTPS connections for posting status updates and other interactions. Because some servers are not configured correctly to handle making HTTP queries, I've included a toggle so that you could switch WP to Twitter to make queries on HTTP instead of HTTPS.
As of January 14th, 2014, Twitter has shut off HTTP access to their API. 403 errors will now be returned when an HTTP query is made, and your status update will be rejected.
If you have been dependent on HTTP support, you'll need to talk to your hosting company about fixing the problem. I'm afraid that there's nothing I can do.