Twitch Support has stated that at the present time, they have received no ETA from Microsoft as to when Xbox One Direct Broadcasting will be available.
The update came from Twitter, with Twitch saying "Xbox One Direct Broadcasting: There is no ETA at this time from Microsoft. Expect a few more months. If we know sooner, we'll update."
Twitch was prpmoted as one of the core features that gamers expected from the Xbox One, especially as it was promoted as a social gaming platform. However, the service wasn't available for the system's launch in November.
At the time, Microsoft stated they would work to try and get the service up during the first part of 2014. However, as time goes on, this is looking less likely.
Despite the unknown issues with the Xbox One, Twitch live broadcasting launched alongside the PS4 in November. Twitch themselves have now stated that towards the end of December, 20 percent of their streamers were using the PS4's interface. This was a marked increase compared to the start of the month, when this figure was only 10 percent.
This figure alone shows that the longer the service isn't available on Xbox One, the larger the market share PS4 games will have on Twitch.