Popular Sovereignty was appealing as a solution to the very emotional and controversial debate about slavery before the Civil War because it was a compromise approach that allowed each state to decide its position on slavery rather than making slavery a federal issue. Basically it was seen as a way of avoiding this controversial and potentially ruinous issue at the Federal level. The idea of Popular Sovereignty was conceived during the 1840's but it was Stephen Douglas who pushed the concept in the Compromise of 1850 and the Kansas-Nebraska Act. The concept was not really effective at preventing war however. In Kansas, for example, men who were concerned with slavery as far away as Massachussets sent settlers there to fight for the territory to be anti-slavery while southerners who were pro-slavery also sent their own representatives to the area resulting in bloody battles. Furthermore, the status of slaves whose owners travelled to the North became a flashpoint for both slave owners and abolitionist. The biggest problem with Popular Sovereignty was that it never attempted to answer the moral question of slavery which could not change with state boundaries. This answer would never be acceptable to the true abolitonist who believed that all slavery was wrong.
Some states were in favor of popular sovereignty as a way of asserting authority in contrast to the power of the federal power and also as a way to protect their economies,which were heavily dependent upon slave labor.