Lincoln was against slavery but he was not looking to outlaw the practice. Even the emancipation proclamation only freed slaves from the territories in revolt (the Confederacy). A big part of the issue was State's rights versus Federal rights. There had been problems with tariffs as well as discussion on where to build the national railroad. One of the main issues was the idea of nullification. This was the idea that states could choose to "nullify" any federal law they wanted. The federal government did not agree with this as it weakened its power. Many States in the South believed they should be able to nullify certain laws such as tariff laws that hurt their economy. This was one of the earlier disagreements between the North and South that led to the South to secede.
Lincoln and other Republicans were against the spread of slavery. Remember that at this time was the United State's "manifest destiny" and settlers were traveling and forming new territories and States. There had been a compromise for allowing some states to become slave holding states but there were still many concerns about which territories would become slave or free. It became a question of geography (north and south of the "mason-dixon line") and if the amount of states accepted should be limited to keep a balance in the Senate of Free and Slave states. In this sense Lincoln was against the spread of slavery to new states and territories. Also consider all the issues legally that came up when people with slaves crossed to non-slave territories and states. Were the slaves free because they crossed into a new territory? Were free African Americans suddenly slaves or liable to become slaves if they passed into a slave state? There were many legal cases over this issue at the time.