Popular vote tied.
After the Great Realignment of 2012, with the election of Republican President Mike Huckabee, the GOP becomes the populist party and in effect forces the Democratic Party to become a moderate libertarian party. Huckabee enjoys a successful tenure and as a result the Republicans see electoral success. In the 2012 election the differences between the parties and their new identities becomes very clear, with the big states of California, Texas, New York, Pennsylvania, and Florida all becoming swing states. The end result is an electoral tie that causes it to go to Congress.
The House Vote:
The Democratic nominee wins 26-24, however, the Republican ticket wins the Vice President after going through the Senate. The first biparty administration since John Adams and Thomas Jefferson takes place.
When I'm not so tired I'll do one where the opposite happens, Reps become more libertarian, Dems more populist.