In the United States, the two party political system is firmly rooted in the structure of governance and in the minds of the people. In the current immensely polarized United States, much of the general populace strongly identifies with one party or the other. In the chaotic state of the current sham of a Presidential race is there room for the rise of a third party? In short, the answer is no it is strongly unlikely.
In political science there is an established theory called Duverger's Law which attempts to explain how certain electoral systems favor different types of voting. It was first published in 1951 by Maurice Duverger and has since been the focus of vast amounts of research. Duverger's law states that plurality rule elections in single-member districts tend to favor a two-party system while multiparty systems are favored by proportional representation. Simply put, the type of election system in the United States over time develops a voting pattern that discourages third parties.
In a single member district are prevalent in the United States. These districts produce one winner per region to send to the legislature. These districts tend to produce fierce competition which sways voters to vote in a way that may not be necessarily in line with their beliefs. These votes are often based on which candidate is most likely to win and who is closest to personal values. Over time the steep competition promotes two competitive parties of wide platforms that voters can more easily identify with one facet or another.
Proportional representation is self explanatory, seats in governments are determined by the percentage of votes in the overall country given to each party as long as they are above a certain percentage. This type of system grants a more realistic division of power between large catch all parties, designed to gain as many votes as possible. and specific value smaller parties like the Green party. It also has a tendency to allow fringe groups greater power as many political parties under the proportional system are forced to make coalition governments between two or more parties to gain the necessary number of votes to take control of the government. More importantly, it grants the ability for a large portion of the population to vote for candidates that more closely resemble their values.
In the past, political parties have experienced cycles of rise and fall akin to the cycles of a rock star. Most of the famous older parties are well documented. The rise and fall of the Whig party, the loss of the core tenants of the Lincoln-era republican party, the fall of the federalists. In almost no instance is there more than two large scale parties at the state level, none at the federal level. It would take a colossal effort to upend decades of Democratic and Republican competition for a third party candidate to win at a federal level when they so often lose on the local level. Voting for a third party candidate at the Presidential level is akin to voting with an absentee ballot. Both are largely discounted and have very little impact in the US. In this hotly contested and largely embarrassing race for President, voting for a third party candidate is not viable. If for some reason, Gary Johnson or Jill Stein succeeds in a David versus the Goliath esque fashion, it would upend a large swath of research which, while not necessarily being a bad thing, would certainly be confusing to those in the field of politics.