Probably. See post #12.
Parties will continue to exist, they just won’t have as much power. They have been losing power for the last 50 years. Primaries instead of back room deals determine who the nominee is and the party is powerless to stop it. The Democrat party apparatus still has a little power in the presidential nomination process because of the superdelegates but not that much. In 2007 I heard a speech by someone who had worked very high up in both the media and political areas. He said that Hillary had the nomination for 2008 sewn up because she had the backing of her husbands money people and the endorsement of every meaningful democratic officeholder in the country. Then people started voting and Obama beat her like a rented mule.
This year Hillary is doing much better thanks to the black vote which tends to be very establishment, but Sanders is doing very well despite have very little backing among the liberal money establishment and being personally disliked by just about every prominent Democratic politician.
The Republican party has even less power, the two top candidates are Trump who has a registered Democrat until 2009 and Ted Cruz who has gone out of his way to make every other Republican senator dislike him. In fact, he touts their dislike of him as one of his greatest assets.
Parties don’t hand out money any more, campaign finance laws and the internet have changed that. Endorsements mean almost nothing since the internet makes it easy to communicate directly to voters. The only thing the parties have of value is ballot access and by their own rules they have to give that to whoever the voters choose
This means more cranks and loose cannons like Trump, Sanders, and Ventura will run and do better than ever.
Here in New England, third party candidates can be viable. Bernie Sanders was an independent Senator and Mayor for many years before coming to the democrats. Maine has had several Independent governors, and one of them (Angus King) is now in the US Senate. The green party also does pretty well here.
I could see a rise in third parties at the local and state levels. Federal, not so much.
In addition to the rules regarding representative districts, the executives of the federal and every state government are independently elected. Unlike Canada, where the Prime Minister and the premiers are selected from members of parliament. In Canada, a third party can act to form a coalition with one of the other parties, trading votes for a voice in the government. While Canada has seen far fewer coalition governments than many European nations, the possibility, (or threat), is there so that the third party must nearly always be considered when forming policy.
Under the independent executive structure of the U.S., the president or governor is under no threat of a vote of no confidence and may continue acting on his (or her) own throughout the term of office. Thus, there is no power of persuasion that a third party may wield in the U.S. and nearly all third parties have shriveled and died in less than a decade, for a lack of an ability to accomplish any of their stated goals.
However, badly the Republicans and Democrats may fracture in the next election or two, the re-assembled political landscape will be dominated by two parties.