A third party candidate tipped the election of 1844 to the 'Rats and the result was the Mexican War. A third party candidate in 1912 tipped the election to the 'Rats and we wound up being dragged into WWI.
A third party candidate (Pat Buchanan) almost tipped the 2000 election to Gore. Instead of wars in Afghanistan and Iraq and a War on Terror, we would have had national self-flagellation after 9/11, efforts to apologize to the Muslim world, a war on global warming, and perhaps a war on Christian "intolerance" of Islam.
So third party candidates can make a big difference even when they draw paltry numbers of votes.
Not there was anything wrong with the Mexican War....