The establishment of the Republican Party was a major factor in the start of the Civil war. The Republican Party was established in 1854 by many ex-Whigs and ex-Free Soilers and was expressly against slavery. Of course, Abraham Lincoln was the first Republican president. It was his election that convinced South Carolina to secede from the Union. Because the Republican Party was an anti-slavery party, South Carolina, along with other southern states, saw the election of a Republican as president as a direct threat to the institution of slavery. And they saw this threat to slavery as a threat to their whole economy since the southern economy was based on cotton and the production of cotton was based on slave labor.
In my opinion, the main impact of the change in party alignments was to hasten the coming of the war by making compromise impossible.
The change I am referring to occurs when the Whig Party breaks up and eventually gives rise to the Free Soil and later the Republican Party.
Before this change, the Whig Party, like the Democratic Party, was a national party. Both parties were pretty strong in the North and the South. The Whigs broke up, however, largely along sectional lines -- the Northern and Southern Whigs could not continue to find common ground.
When this happened, the parties moved towards a North-South split. When Lincoln won his presidential election, he go no Southern votes. His party was a Northern party only. By that time, the Democrats had run a Northern and a Southern candidate as well.
So the parties realigned along North-South lines and that made compromise impossible.