If the 7-10 million number is correct, we still need to ask where were these voters staying home? In Texas? Oklahoma? Or did they stay home in Wisconsin, Ohio, and FL? The election was only really contested in 7-8 states, so a decline in voting in the other 40+ states would not be consequential.
South Carolina saw less than .1% voter dropoff comparing 2012 to 2008.
2008 total votes: 1,897,345
2010 total votes 1,895,263
Romney percent of vote 55.4%
McCain percent of vote 53.9%
No descernable purist or religous backlash seen from these numbers in South Carolina. However, there is no evidence of a massive wave turnout for the GOP either. Maybe someone can do similar stats for Ohio and Virginia, but my thought is that Team Obama simply did a surperior job of identifying their voters and getting them to actually vote in the swing states.