United States political history (at least its first half century) was punctuated by collapsing party systems. Political parties organized, pursued their specific agendas, and then fell apart. They declined because shifts in the electorate left a party out of touch with the issues that animated people's political participation or because internal divisions overwhelmed what the party held in common. Alternate parties arose and pulled voters away from the two major parties. Today some historically informed commentary suggest that 2016 might witness another collapse, as the GOP fractures over the runaway popularity of the rogue Republican candidate Donald Trump. See http://www.rollingstone.com/politics/news/why-the-2016-election-will-be-one-of-the-most-pivotal-moments-of-our-time-20151203?page=15. Differences between the parties in the early nineteenth century and now may mean that those who hope to see a GOP collapse are in for a disappointment.
The first clear political division to form in the United States split Federalists and anti-Federalists, those who supported and opposed the radical revision of the central government proposed in the U.S. Constitution. Once the Constitution was adopted, the reason for this party rivalry disappeared, and the anti-Federalists ceased to exist as an organized entity. Very soon, however, Federalists (in a somewhat altered composition) upheld a powerful federal government, the economic development of the U.S. and alliance with Great Britain against the Republicans or Democratic Republicans who favored revolutionary France and took the opposite position on each of these issues. The Federalists eventually declined, especially after they tried to withdraw New England from the Union (in a northern move prefiguring the separation in the later Civil War). Another party pairing eventually arose, in which Whigs opposed Democrats over financial policy (especially a national bank), but disappeared in the factional disputes over slavery. By the outbreak of the Civil War both Republicans and the Democrats existed, although the latter suffered from a sectional split. Their politics at the time were not aligned with their positions today: Republicans fought for an end to slavery and the inclusion of African Americans in the political nation (as well as for the development of industry and infrastructure), while Democrats opposed an intrusive central government, sought states' rights, and opposed a confrontation over slavery or, later, rights for former slaves. Yet these parties were nonetheless the antecedents of those we have today.
While this kaleidoscopic alteration in the party landscape seems to suggest that the current parties might cease to shape American politics, the parties themselves have worked over the last century and a half to insulate themselves from collapse. Party structures are much stronger and more entrenched. Parties wield power separate from their voters in a way that early party organizers did not. They have full coffers, extensive bureaucratic structures, and a formal role in the political life of the nation, all supporting their continued existence. So, for example, the offices of Minority/Majority party leaders in Congress--which are not part of the Constitution and were not anticipated by the founders--are now so much a part of our political system that most Americans do not realize they were a relatively late addition, a creation of the 19th century, arising after the Democrats and Republicans became fully realized political players. How parties with such power would vanish is not apparent, and certainly earlier cases of party collapse offer no analogous precedent.
If you are hoping that the Republican/Democrat lock on American politics will be torn asunder in the coming year, be warned that the path to such an outcome is not as well-worn as some would suggest. Collapse may come, but what that would look like is anybody's guess.