A while back Twitter announced that any URLs being shortened by its t.co service were going to cost users two extra characters. When you only have a 140 characters to begin with, the extra characters could be disastrous when trying to get your point across in a tweet.
It seems Apple didn't take the change into account with its integration of Twitter in OS X Mountain Lion. I discovered this when attempting to tweet a link from Safari. According to the tweet sheet, I had composed a perfect tweet, using up my entire 140-character allotment.
But every time I clicked send, I'd get the above message. I knew Twitter wasn't down, as I was able to access it just fine via Tweetbot. So I copied the text of the tweet from Safari into Tweetbot and manually entered the URL. It was then that I realized the problem; according to Tweetbot I was two characters over the limit.
I went back to Safari, composed the same tweet, save for the last two characters and the tweet sent without issue. So if you find yourself tweeting a link from OS X, be it from Safari or Notification Center, and keep receiving an error message, try deleting a few characters from the tweet and sending it again. Hopefully Apple fixes this minor -- yet annoying -- bug in the near future.