The problem with the question is the problem with the whole left/right spectrum in general. There are so many issues to be considered, and more than a few demographic groups as well - and they don't always band together.
On social/race issues the big flip came around 1964 with the civil rights act. In terms of pragmatism vs. ideological purity they have all but completely flipped over the past two decades. In terms of demographics, Democrats are attracting a larger number of the well educated while Republicans are attracting more people with less education.
In economics it's a bit lopsided, with Democrats largely for free markets and Republicans supporting corporate cronyism (socialists are almost non-existent in American politics).
