Just wanted to post some updated information about this. Google has released the API / SDK publically now and it is available for anyone to use. https://developers.google.com/cast/
While it's main focus is to still 'point' the chromecast to a server and pull down it's contents directly, there are many apps which are currently able to stream local content from your device, for instance a local video on my nexus 4, directly to the chromecast. This does appear to be available functionality through the SDK.
I would love to see this functionality added for my home. I currently own 2 of these devices with plans for a 3rd. With the releases of the SDK, is functionality is increasing at a very rapid rate and is quickly approaching a level where in the next few months it will rival device such as the roku in its abilities for half, or less, the cost.
(For those looking for a way to stream those longer videos available on LDS.org that aren't available on YouTube, you can download the video to your device and stream it to your chromecast using an Android app called AllCast, EzCast, or several others which you can find it in the Google Play store. There are also apps in the iTunes app store as well for iOS users.)