You have the answer to this in the tag that you put on here -- the first political party in the United States to split over the issue of slavery was the Whig Party. This party split up for good in 1856.
The Whig Party had started up back in the early 1830s. It was a party that drew people from all parts of the country, mainly (at first) because of their opposition to Andrew Jackson.
The break up of the Whig Party was finally caused by the Kansas-Nebraska Act of 1854. The debates over the law caused Southern Whigs to break off and join the Democratic Party while Northern Whigs generally went over to the new Republican Party.