Another explanation, the most logical, is that the six million Evangelicals who voted for Obama look like Obama also.
If that is true, we are not talking about Evangelicals are we? Sorry, there is a major difference in beliefs here...
Romney didn't get up to McCain's numbers, so we have a 2 million vote gap.
The difference is readily explained by demographic change, death, disease, disability ~ etc. Someone forgot to register more Republicans and then encourage them to go vote for the Republican candidate. I think that's behavior not really of much interest to the GOP-e ~ they leave it to the locals ~ even if Romney had kicked sand in their faces ~ does not work well!
Evangelicals voted. Black Evangelicals voted for Obama. They were at least 10% of his vote ~ to wit, 6 million people.
White Evangelicals voted for Romney ~ probably in greater percentages than other groups ~ even Mormons.