They wanted to be the Get Along Gang.
The Republicans came in and said "NO!" To the Kansas-Nebraska Act or whatever Trick the Dem's were using to expand Slavery to the West.
Because the Whigs wheeled and leaded to limited the growth of governm-, I mean slavery only made things worse, finally when it became Clear that the New Republican Party didn't need any of Slave states to win the Presidential Election of 1860, the south said "To Hell with this" and the rest is history.
So it splintered into anti-Democrats, Free Soilers and Know-Nothings.
Only after the Whigs collapsed did the Republican Party become a national force.
The GOP did not begin as an organized, coherent faction of the Whigs who took the Whig Party over and then transformed it from within.
Nor did the GOP begin as a breakaway faction from the Whigs that contested elections as a third party against the Democrats and Whigs.
The GOP was a response to the chaos that ensued when America had only one organized national party left - the pro-slavery Democrats.
The GOP was a response to a power vacuum.