Were you hoping to gather 'round the flatscreen and Chromecast with your local Android Users Group for the live stream of Google's next Nexus event? Too bad: at the moment, YouTube live stream videos just won't work with Chromecast, as demonstrated by our tipster Nathan. We tried it using the Lollapalooza 2013 live stream, and sure enough, it just won't display.
This lack of functionality is documented in Google's support page as well, though the reason isn't clear. Videos set to "private" and videos disabled for mobile viewers are likewise inaccessible (remember that Chromecast is running a modified version of Android) no matter what device you "cast" to your TV, or from what account. Interestingly, sending a live stream to Chromecast from a desktop or laptop with the full Chrome browser will let you listen to the audio and see a few choppy frames, but it isn't close to satisfactory. Google may address this with a future update, or they may not - I can't imagine that these relatively narrow use case scenarios are much of a priority.
On a personal note, I can report that using an Android device as a mobile WiFi hotspot also won't work - you can't "cast" from your phone to the Chromecast when it's being used as the Internet connection. You can work around this by having another Android device or laptop handy, but that makes it even harder to enjoy the Chromecast while traveling.
Source: Google YouTube Support - thanks to Nathan for the tip!