A peaceful solution was not possible for slavery, as the US government tried to solve this problem several times before.
One way they did this was through the Missouri Compromise (1820). This law established a border to show citizens where slavery would and would not exist. Any new territories above the 36'30 line would be territories where slavery was not allowed. Any new territories below (aka south) of this line would have slavery. This does not fix the problem, as the US adds several more states above this line, throwing off the balance of free and slave states in Congress.
To try to fix some of these problems, Congress passes the Compromise of 1850. This compromise allows for California to enter as a free state and gets rid of the Missouri Compromise. Along with this, a new fugitive slave law is passed. This is supposed to make northerners return runaway slaves to their owners. However, this does not work well as many northerners ignore this law. Southerners, on the other hand, ignore the north laws about bringing slaves into their territories.
These examples show that the US needed to figure out whether it would be a slave nation or not.