Every 30-40 years, there's a major shift in the political landscape of the United States. As the image below shows, the last major shift came in the 1960s when the southern states flipped from voting Democrat to voting Republican and New England began trending back to voting Democrat. We are now over 50 years into this political landscape and both parties are ripe for a major pivot in policy and platform.
The shift in the 1960s saw a push to a more social-liberal Democratic party and a more social-conservative Republican Party. This system sees the rise of the "Moral Majority" supporting the Republican Party while the Democrats become the party of the minorities and social liberalism. Democrats characterized by social justice and a semi-regulated private market embracing social liberalism with a populist, pro-worker, pro-collective rights ideal. Republicans characterized by social conservatism and the rights of the state, pro-business, anti-immigration.
What's next?
In this modern era, disagreements seem to be focused more on whose rights rather than the right itself. Abortion is the rights of fetuses vs rights of pregnant women. Republicans are bigger on religious freedom (things like freedom of conscience for religious institutions not having to support birth control and abortions and whatnot in their insurance plans) and the rights of private businesses. Democrats are bigger on the rights of people to not be discriminated against by private businesses and don't really care about religious objections to providing things like birth control (because they ultimately care more about the positive right of access to those things). There are also property rights vs. the right to homeland security.
This is good news!
For all the doom and gloom, the fact that we've moved away from arguing whether people have certain rights means we are making progress. Both sides are at least fighting for a groups' rights instead of fighting to oppress a group (though this is still a problem on certain issues).
What I see happening is the emergence of a socially liberal, fiscally conservative party. It could be the current Democrat or Republican party that makes the shift. Once this happens, the other party will shift further away from that and either take an extremely progressive or extremely conservative position, hoping to consolidate the base and slowly draw voters away from the middle. Either way, we are in for a big shift very soon and I can't think of a better catalyst than a Trump/Hillary presidential race.