What if the Republicans in 2012 had nominated Rick Santorum in their primary, and he proceeds to lose by a wide margin to President Obama?
I'm thinking he picks Bob McDonnell to be his running mate thinking that a work-minded southern governor is a good balance to his rust belt catholic social conservative politics. The press then digs around and discovers McDonnell's corruption earlier. Cross that with Santorum responding poorly to Todd Aikin and Richard Mourdock, and the GOP doesn't fare well that year.
President Obama wins North Carolina, Arizona, Georgia, and Nebraska's Second Congressional District and likely wins the popular vote by 7-8 points like in 2008.
Jeff Flake and Dean Heller lose their Senate races, meaning the Senate is 57-43 afterwards.
Democrats win the popular vote in the House by 2-4 points instead of by 1 point. The GOP maintains control of the house by its fingertips probably due to gerrymandering.