An Emergency Broadcast System for Twitter might look like this.
When everything is working at Twitter, all the clients communicate through Twitter. A client is an app like Tweetdeck, UberTwitter, Seesmic, Brizzly, Tweedroid, etc.
However, when Twitter is down, each client sends your tweets to a "safe place" and the clients your friends use hear about your status updates from there.
There's still a lot of disruption, but some messages get through. Over time the EBS will get better, as we learn better how to make the best of a Twitter outage.
Reality: We still need to communicate even when Twitter is down.
Bottom-line: The client vendors are key.
5/20/10: "The secret for the client guys is that instead of investing in individual platforms owned by huge corporations, they must swallow hard and invest in working with each other."