Historical precedents give little encouragement for those who would replace a major political party in the United States.
1. The Federalists all but dissolved after 1816, ushering in an "Era of Good Feeling" that lasted until the 1824 election. Some former Federalists and former federalist issues reemerged, along with former Democratic Republicans and newly important issues, in the "National Republican" party in the late 1820s. That party merged with other disaffected opposition factions in 1833 to create the Whig party.
2. Both the Whigs and the Democrats split over the slavery issue in the 1850s. The Whigs split up over slavery in 1852 and basically stopped operations, with many of their members leaving politics for a time. Some later formed the Republican party, others the Constitutional Union party, with some of both persuasions passing through the nativist Know-Nothing party. By 1860, the Democrats were split more evenly than the former Whigs were, letting the Republican party have a plurality of the presidential vote. After secession, a bloody civil war, years of military government and then the abandonment of Black citizens' rights, by 1877 the Republicans established themselves as the nation's preeminent party.