Twitter’s statement on push notifications, as reported by TechCrunch:

We’ve been testing push notifications internally. 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. So, push isn’t ready yet but we look forward to rolling this out soon.

I’ve been using Boxcar for Twitter push notifications, but it can be a little flaky at times. If Twitter could roll push notification functionality into their own app, I’d be all for it.