In my opinion, 2012 was the first presidential campaign in a long time where the Republicans did not try to use divisive social issues to win, and instead focused on their economic plan (cut spending/cut taxes for rich people). The problem is that their economic plan is unpopular, but in large part Republicans have been able to hold power and pass that agenda because they were able to divide people with those hot button issues. With America moving toward the other end of those issues, Republicans are either going to have to find some new things to scare people about, or change their policies to be more palatable.
What makes you think people are moving to the left?
It's not really "moving to the left" so much as it is the fog clearing and people having a more clear view for economic issues.
Things like same-sex marriage becoming more socially acceptable is part of that. It's no longer going to be a wedge issue for Republicans to capitalize on, as seen when
Ted Cruz just said that he believes it's up to the states to decide.