Something like that could be achieved using the FlexMenu in our latest version. However we don't have a step by step or tutorial for it at the moment. The ChildNodesPerUl property would control how child li elements are split into multiple ul elements. A good designer should be able to figure it out from the documentation and by experimentation.
This menu control goes a long way towards automating a nice mega menu type menu from the site map, but if one needed complete control over the markup and needed to inject arbitrary stuff in arbitrary places at arbitrary depths one might have to hard code raw html for the menu. I suspect the one on whitehouse.gov is lovingly crafted by hand since viewing the source I can see commented out sections.
Hope that helps,