As parties ignore their core constituency in favor of special interests, third parties come about that splinter from the main. The GOP was the surving splinter group of the Whig party in the 1800s, where it was still a "3rd party" when Lincoln was elected. In fact, Lincoln wasn't even on the ballot in the southern states. There were two splinter groups from the Whigs and one splinter group, Southern Democrats from the Democratic Party, that went up against the Democratic nominee.
In 1912, Republicans rigged the convention against Twddy Roosevelt on favor of his successor, Taft. TR got more popular vote, as well as electorial college votes, than Taft, and, had he run as a Republican, would have won in landslide. The only reason Taft got the support at all was party voters. It cost them the election.
Third parties do sway an election. Depending on how well Hillary's corporate bosses can rig the general election (usually, they can) expect her to be elected. Otherwise, we have Trump.
We no longer vote FOR a president, we vote against the person we don't want to be president.