Seward and Lincoln were right in stating that the US could not exist as half slave and half free. The US tried this multiple times, but there was always a conflict that arose.
Take for example the Missouri Compromise. This law, made in 1820, said that any territory north of 36'30 coordinates would have no slavery and any territory south of this line would allow slavery. This was a very temporary solution, as the US continued to gain territory. The US gaining territory would threaten to change the balance of power in the US Congress. To make sure this didn't happen, the government replaced the Missouri Compromise with the Compromise of 1850.
The Compromise of 1850 made California a free state, got rid of 36'30, and developed a new fugitive slave law to help slave owners retrieve their slaves. However, many northerners refused to follow this law. On the other hand, many southerns brought their slaves into free territories thanks to the Dred Scott ruling.
These events show that eventually, the US would have to decide on being a slave nation or a free nation.