I've seen that issue as well, most often on Firefox, but sometimes in Chrome. I think the issue is that the CesiumWidget is constructed before the DOM is completely laid out, so the browser gives us the wrong size from clientWidth/clientHeight is incorrect, and we never get a resize event, since the window size hasn't changed.
I had a similar issue in the 2012 NORAD Tracks Santa app, which I worked around by basically forcing a resize periodically during the render loop after some number of frames, milliseconds, I forget which. The reason we don't resize on every frame is that accessing clientWidth/clientHeight forces a layout, lowering performance.
At the least, we should make the resize method public to allow client code to call it after changing the DOM.
Scott