Want to make your own basic map with election results and some demographic layers? See my tutorial on How to make an election map in R, in 10 (fairly) easy steps
Want to see how the pros at Esri map Super Tuesday demographics with ArcGIS? The map below shows overall demographics and state-by-state political leanings; click on any county to get more detailed data such as population, median income, unemployment rate, party affiliations and a demographic category based on factors such as population growth, population density, housing affordability and socioeconomic status. (Note: May take a little while to load).
My main quibble is that this maps party affiliations by map area without taking into account population density, so large rural areas with few people look more important than smaller, more densely populated urban areas. It's the same issue I discussed in my tutorial, and thus why I like to generate my own maps with data points that are most interesting to me. And since I already use R, I don't need to learn another software package and have one platform for acquiring, re-formatting and visualizing data. On the other hand, the Esri map is a lot prettier than mine! And, there's some interesting per-county data available if you click through on the state levels: