The good news is that just like the Year 2K panic, this one is more or less unfounded. We've already spoken to our friend Ged Maheux of Twitterrific, and he says that the problem has already been fixed in the latest version of the software. We'd imagine that most of the really big Twitter apps have already addressed the issue, and taken care to make sure they'll still work (either that, or they'll get on it ASAP). Plus, a Twitter outage wouldn't really be anything that might cause riots in the streets (or different from the usual downtime, actually -- rimshot!).
But it is funny and strange that as long as we have people who can't foresee the future (so, all of us) programming computers, we'll keep running into problems like this. If your favorite Twitter client goes out on Saturday, just find a basement to stay in, stock up on shotgun shells and water, and put your head between your legs -- help is on the way soon.