Ooh, another "it's just a weekend project!" comment.
Next step: convince everyone to use your weekend project, instead of Twitter. Allowing people to import all of their tweets and friends would be helpful, so be sure to implement that.
Next next step: Handle all of Twitter's traffic. Consistently, and you not only have to do it better than they did in the beginning, but better than they do it now.
Here's the thing. If it were anything other than a major endeavor to replace twitter it would have been done by now.
It is a big problem and not just from an engineering standpoint. The same for facebook.
On the plus side, for competition at least, as hardware technology advances it'll become easier and cheaper to match twitter's capabilities with less effort.
Next step: convince everyone to use your weekend project, instead of Twitter. Allowing people to import all of their tweets and friends would be helpful, so be sure to implement that.
Next next step: Handle all of Twitter's traffic. Consistently, and you not only have to do it better than they did in the beginning, but better than they do it now.