In White Voters in 21st Century America, I argued that the decline of union membership is one important reason non-Hispanic whites have been trending toward the GOP in recent election cycles, largely offsetting the Democratic gains among the growing minority population. For whatever reason, union membership did not seem to have as strong an effect on non-whites -- though I would have to look at some new data to see if that is still true.
Union coverage does appear to be a powerful predictor of the white vote at the state level and at the individual level. As an illustration of this, here is a figure showing the relationship between McCain's share of the white vote (based on exit polls) and union coverage at the state level:
This is definitely one of those nice, mostly linear relationships that political scientists do not see very often. I should note that I have a better figure from 2012, which focuses just on middle-income whites. But I am not going to post it here yet to avoid any headaches associated with trying to publish a paper with a figure that has appeared elsewhere; it is part of a paper I hope to submit for review soon.
I should note that this figure is not simply the result of Southern states being both pro-Republican and anti-union. When Southern states are dropped, the figure looks quite similar.
This is relevant because union membership has continued to decline over the last eight years, and it has declined more in some of the states that the GOP is most hopeful to turn from blue to purple. The most glaring example is Wisconsin. The anti-union legislation that Governor Walker enacted clearly had its intended effect. From 2010 to 2015, no state saw such a dramatic decline in its union coverage -- a drop of over five percentage points, according to the Current Population Survey. All the other states in the electoral vote rich Upper Midwest saw declines in their union coverage rates. Union coverage dropped by 1.1 percentage points in Ohio, 0.8 percentage points in Michigan, and 1 percentage point in Indiana. It also dropped by 1.5 percentage points in the important state of Pennsylvania.
If the relationship between white vote choice and union membership is not spurious (and I don't think it is), we could see the GOP further improve its share of the non-Hispanic white vote in 2016 compared to 2012. Unless there is a similar movement of minorities toward the GOP, then such a development would only further exacerbate the trend toward racial and ethnic polarization in American politics.
On the other hand, there are a lot more variables at play this year than just the decline of unions.