following the mexican-american war, which issue broke party unity and divided congress largely along sectional lines

The extension of slavery throughout the recently acquired lands or territories from Mexico.

After the Mexican-American War, the main issue which broke party unity and divided Congress largely along sectional lines was the issue of the expansion of slavery into the territories that previously belonged to Mexico. As a result of the war, the United States was able to acquire large amounts of territory. However, these territories now needed to decide whether to allow slavery or not. This was a delicate issue, as it could upset the balance of power in the Union.