Twitter is struggling to overcome a denial-of-service attack, they wrote this five hours ago:

We are defending against a denial-of-service attack, and will update status again shortly.

Update: the site is back up, but we are continuing to defend against and recover from this attack.

Update (9:46a): As we recover, users will experience some longer load times and slowness. This includes timeouts to API clients. We’re working to get back to 100% as quickly as we can.