Viable third parties in the United States are the result of dissatisfaction with one of the two primary parties, and in US history they have even replaced one of the two primary parties. The Republican Party did so to the Whig Party.
I can see the current Republican party having a strong possibility of splitting into a more populist Tea Party sort, and a more establishment Republican party remain. There is a chance that if it does split, it might break into multiple parties--a more evangelical, religion-based party, a party focused around nationalism, and one with greater interest in economics. I'd expect the Libertarian Party to pick up many disaffected former Republicans in such an instance.
The Democrats have a small chance of fracturing, too. The Clinton/Obama wing is socially liberal but economically center-right. The more progressive Democrats--the ones who supported Sanders--could possibly foment a breakup and new party, if the Republicans did so first. Why? A smaller but truly progressive party would have a much greater chance to win an election if the two primary parties disintegrated.
I don't see either possibility as likely, but the Republicans splitting is much more possible.
As far as viable 3rd parties...no. Until we get money out of politics, smaller parties will never have a chance against the big two, which are both supported by inertia, tradition, and scads of money from the elite.