Video streaming over websockets using JavaScript

The Media Source Extensions has been proposed which would allow for Adaptive Bitrate Streaming implementations.

Is WebSockets over TCP a fast enough protocol to stream a video of, say, 30fps?

Yes.. it is, take a look at this project. Websockets can easily handle HD videostreaming.. However, you should go for Adaptive Streaming. I explain here how you could implement it.

Currently we're working on a webbased instant messaging application with chat, filesharing and video/webcam support. With some bits and tricks we got streaming media through websockets (used HTML5 Media Capture to get the stream from our webcams).

You need to build a stream API and a Media Stream Transceiver to control the related media processing and transport.