The Know Nothing Party had essentially dissipated by 1860. It emerged in the 1850s after the Whig party collapsed in the wake of Bleeding Kansas, and its main cause was espousing anti-immigrant and anti-Catholic sentiments. There was a large influx of immigrants to the US at this time, especially due to the Irish Potato Famine. After the Dred Scott decision in 1857, the party largely merged with the Republican Party due to increasing opposition to slavery.
The Free Soil Party, like the Know Nothing Party, was a single-issue party that had mostly died out by 1860. Free Soilers opposed the expansion of slavery into new territories in the west. They arose mainly in the aftermath of the Mexican-American War, when the US added new territories that could potentially become states. With each new addition, the question of whether or not to allow slavery brought up fierce debates. In order to avoid the divisive nature of abolition, many Free Soilers instead argued that slavery should be banned from the west because it would mean fewer opportunities for freemen and was therefore economically detrimental. This party largely died out after the Compromise of 1850 temporarily eased tension over the extension of slavery. Many Free Soilers instead joined the Republican Party.