Nope, there was no Whig Party in 1860.
The last presidential election where the Whigs were at all functional was 1852, when they got 42 of 296 electoral votes.
They were largely replaced by the Republicans in 1856 as the opponents of the Democrats, when they ran Fremont. That year the Democrats got 174 electoral votes, the Republicans 114, and the Whigs the grand total of 8.
By 1860 “the two parties” were the Democrats, who split themselves three ways, and the Republicans, who stayed united. The Whigs didn’t exist.
So you’re telling me that the Republicans went from zero representation in 1852 to respectability in one election, 1856, and to victory in 2 elections, 1860.
That means a new party can be grown pretty quickly.