How did opinions differ over how to end the institution of slavery?

In the Constitution, slave importation was actually set to end in the early 1800s. Many had hoped this would end the practice as no more slaves could be brought in. However, there was nothing about the children of slaves. The next idea was to contain the practice of slavery. This was done thru different actions like the Missouri Compromise of 1820, the Compromise of 1850, and the Wilmot Proviso. While all of these were going on there were also people who wanted the entire practice completely banned and labeled illegal. 

Possess private property.