a couple days ago for the iPad, there were apparently a small portion of users who managed to experience a much wanted feature that's going to become available soon to the masses. They were actually able to receive push notifications for a brief time, but unfortunately it looks as though it has been pulled completely. Nonetheless, Twitter did come out to indeed confirm that it is coming some time down the road for their iPhone and iPad apps. In the mean time, they're doing some extensive testing in the near term to fine tune any funks happenings with it.
One of Twitter's reps stated, “When we launched Twitter for iPad, there was a configuration error that caused us to offer push messages to a small set of users. We’ve stopped sending push messages, but users may see an option to turn on push until we release an updated version of the app. We’ve been testing push notifications internally. Push isn’t ready yet, but we look forward to rolling this out soon.”