To Winston, almost everything from the telescreen is bad news because he can still think. Every announcement about Hate Week, or war or the fact that he has to get up and do his exercises irritates him. However, one very specific announcement comes from the telescreen close to the end of Book 2.
Winston and Julia are resting peacefully on their bed in the apartment above the shop. Winston is reading aloud to Julia from Goldstein's book. Once again, Julia has fallen asleep on Winston, who is in serious thought about what he is reading. You may remember that there wasn't supposed to be a telescreen in that room. There is. The Thought Police deliver a message to Winston and Julia over the telescreen before they actually come into the room. The message is essentially this: You are dead. I can't think of any worse news to receive.
Funny, Winston after reading Goldstein's book and having a relationship with Julia was likely just beginning to feel alive.