The General Social Survey asked 3,322 people: 1) who they voted for in 2012 and 2) how happy they are, generally speaking. Here's the breakdown:
Percent Very Happy
Obama Voters 27.9%
Romney Voters 36.8%
Percent Not Too Happy
Obama Voters 13.9%
Romney Voters 9.3%
Myself, I'm sad I voted for Romney. But it looks like Rush has a point even if he exaggerates a bit. Personality traits might explain the difference: Liberals are more prone to negative emotions, they are less conscientious (self-disciplined), and both of these predict less life satisfaction.
My bet is that if I looked at social factors, I'd find that conservatives are more religious and more likely to be married, and both predict happiness (believe it or not). Maybe in a later post.