The United States has historically had two large coalition parties. On one side were the Democratic-Republicans which later became the Democrats. On the other side there were the Federalists, National Republicans, Whigs, and Republicans. During all of the turmoil as the parties realigned, they always realigned as two, large, coalition parties.
In the lead up to the Civil War, the Democrats split, which led to the election of Abraham Lincoln and the rise of the Republican party. This split reemerged in the middle of the the 20th Century. However, neither split was permanent, and the spun off third parties never succeeded.
This political centripetal force which pulls candidates into one of only two coalition parties seems to be a component of the U.S. political system. As a result, third parties in the U.S. are not coalition parties, but small, single-issue or ideological purist parties. And as ideological purist parties they are subject to political centrifugal force driving them apart. This has been seen with the many iterations of socialist parties throughout the 20th Century, and also led to the effective dissolution of the Reform Party after Ross Perot left an active role.
Looking at the history of presidential third-party and independent campaigns which gained over 1% of the popular vote, one can see low single digit success of the Socialist Party in the early 1900s (peaking at 6% in 1912) and 1% to 2% for the Prohibition Party in the same era. There seems to be about a 5% third party vote during first 20 years of the 20th Century, with the exception of the 1912 election.
The largest third-party and independent successes were candidates who had split from their main party. Theodore Roosevelt's Progressive "Bull Moose" party run outperformed the Republicans in 1912, with 27.4% of the popular vote and 88 electoral votes, the largest third-party performance ever. Twelve years later, Robert La Follette, who also split from the Republicans and ran under a second iteration of the Progressive Party, won 16.6% of the popular vote and his home state of Minnesota's 13 electoral votes. The 1948 election featured two former Democrats who split from their party: Strom Thurmond with his "Dixiecrat" segregationist party and Henry Wallace who ran on the 1948 version of the Progressive Party. Each got 2.4% of the popular vote, and Thurmond won 39 electoral votes. In 1968, George Wallace split from the Democrats with his American Independent Party, winning 13.5% of the popular vote and 46 electoral votes. This would be the last time a third-party candidate won any electoral votes. In 1980, John Anderson split from the GOP for an independent run, getting 6.6% of the popular vote. In the same election, the Libertarian Party got 1.1% of the popular vote.
The 1992 election featured an independent run by non-politician Ross Perot, who got 18.9% of the popular vote, but was unable to get any electoral votes. In 1996 he ran again under his Reform Party banner and got 8.4% of the popular vote. The fact Perot was not a politician who split from a party meant he drew from both parties voter bases. This prevented him from getting enough critical mass to get any electoral votes. Perot's politics could best be described as populist and centrist. While he did have some social conservative leanings, it was not enough to either gain critical mass from the Republican base, or to turn off the Democrat base. His populist views on trade and taxation likely gained support from Midwest Democrat voters. The Perot/Reform Party of 1992-1996 was probably the biggest opportunity for a third coalition party to form.
Since Ross Perot's runs, the largest third-party results were Ralph Nader's Green Party run in 2000, which got 2.7% of the popular vote, and likely swung the electoral college to Bush, and the Libertarian Party's 3.3% of the popular vote in 2016. Also in 2016, the Green Party got 1.1% of the popular vote.
There are dynamics now which could cause change. Under Trump, the GOP has become a populist, paleoconservative party, very similar ideologically to Pat Buchannon's 1992 GOP primary challenge to George H.W. Bush, and his 2000 Reform Party run. There is no doubt the GOP is suffering an identity crisis. At the same time, the Democrat Party has been in turmoil between its neoliberal interventionist wing and the emerging Democratic Socialists driven by Bernie Sander's primary run in 2016, and Alexandria Ocasio-Cortez's insurgent House primary run and ultimate election. This has caused a trust split between the two groups.
Some of Trump's positions align nearly identically with Bernie Sanders. Some polls suggested 5% of the general election vote for Trump represented former Bernie Sanders supporters. This would translate to about 10% of the Democrat primary voters. Add to that many mainstream Republicans supported Hillary Clinton, who they felt was generally aligned with their views on economics and foreign policy.
A political realignment may be before us. But as both parties are coalition parties, and these coalitions are comprised of components, what becomes of the components neither major party wants?
If a populist-paleoconservative GOP is non-interventionist, and populist-democratic-socialist Democrat Party is non-interventionist, does that open the opportunity for a third party to pick up the muscular, interventionist foreign policy banner? If a populist-paleoconservative GOP favors more restricted trade, and
populist-democratic-socialist Democrat Party favors more restricted trade, does that open the opportunity for a third party to pick up
the free trade banner? If a populist-paleoconservative GOP favors more business regulation, and populist-democratic-socialist Democrat Party favors more business regulation, does that open the opportunity for a third party to pick up the low regulation banner?
While there are a number of areas where the Libertarian Party could gain, the issue of interventionism would likely be a show-stopper for traditional Republicans. At the same time, a majority of the population is exhausted by three decades of interventionism, and a party holding the banner of Realpolitik may gain some interest. Would a moderate middle on trade and immigration be a winning platform, or is immigration now a "third rail" issue?
My personal opinion is our current tax structure at the federal, state, and municipal levels is immoral. Too many politicians want to tinker with the edges to "fix" our economic ills--a tax cut here, a tax increase there. Instead serious foundational structural change will be required, however only a handful of politicians have proposed this: Herman Cain, Rand Paul, Ted Cruz, Mike Lee, and Marco Rubio. Only a few politicians have spoken to how emerging technology is going to radically reshape our future over the next two decades: Ben Sasse and Marco Rubio. You might notice all of these intellectuals or policy wonks I mention are Republicans. There are a small handful of Democrats as well. But futurism, innovation, and business acumen are not qualifiers for political office for Democrats of late. Also, some of these Republicans have polar opposite views on some policies.
My conclusion is the only way a third party will "save us" is if one of the two major parties has a major split, on par with the 1912 GOP/Bull Moose split or the 1948 and 1968 Democrat/Southern Democrat split. Note in both cases, the splits were short lived. A split between the neoliberal and democratic socialist wings of the Democrat party seems possible. Those fault lines are fairly clear. On the GOP side, would the split be between the neoliberals and the economic populists, or between the interventionists and the non-interventionists? Those fault lines are not as clear.
Buckle your seat belts. It is going to be a wild ride over the next 14 years.