In summary, he would give it time and it would end.
In his House Divided speech, Lincoln argued that a country can not remain divided on such a fundamental issue like slavery forever. He argued that one day, all of America must either one day be all free or one day be all slave. He did not forecast that the South would invade the north and spread slavery. Instead, it would be done by Democratic means similar to the Fugitive Slave Acts, the Dred Scott Case, and the Kansas Nebraska Act which rammed slavery rights into Northern Territories. He firmly believed in Democracy and that Democracy would eventually free the slaves.
The key to the power and preservation of slavery was the Senate. Each State gets two Senators. If enough states are free, they could outlaw slavery. For many years, there had been an equal number of free and slave states. Additionally, for many years, the House of Representatives was fairly balanced due to the 3/5ths rule.
Winding back a bit, Andrew Jackson’s Manifest Destiny started a chain of events that upset the balance of Congress and upset the tranquility of Americans.
Territories were acquired and American settlers moved West. New States were formed. States like Michigan were clearly going to be free. States like Texas were going to be slave.
But settlers from Europe didn’t want to move to Southern slave territories. It was near impossible for a poor white to climb the economic and social ladder in the slave States. Most Europeans had a distaste for slavery as it didn’t exist there. Additionally wealthy slave owners were a minority in the South to begin with. As a result, pro-freedom men were moving to western territories in greater numbers then pro-slavery men. They moved to places like Iowa, Minnesota, Illinois, Indiana, and California. Plus New York in great numbers.
This created a problem for the House and Senate balances. The population shifts affected the House. The previous agreements on which territories would become a slave State versus free meant that with all these new settlers, there would be more new free States than slave States.
So, pro-slavery men decided to avoid that.
Senator Stephen Douglas and Senator Atchison broke the past agreements with the Kansas Nebraska Act. They were proponents of Popular Sovereignty / States Rights and argued that each State could decide on slavery itself. It sounded reasonable but was actually a ploy to bring slavery into Territories that were supposed to be free.
This led to Bleeding Kansas which was a proxy war between abolitionists and pro-slavery men from the East. Despite rigging the election and murdering abolitionists in Kansas, and despite support by Senator Douglas and President Pierce, Senator Atchisons army of border ruffians were ultimately unsuccessful. Kansas became free.
The South saw the writing on the wall, slavery would eventually end as it was not spreading as fast as freedom was spreading.
So, they agitated for a war and ultimately started one.
One of the biggest reasons the South has for starting the war was that slavery must spread. What the official Republican platform was that they won’t steal people’s slaves but slavery must be contained to were it already existed.
Interesting, and to further illustrate the point, after the War began and the Southerners left Congress, the Northerners were able to get their way with immigration and infrastructure out west. They passed the Homestead Act and began building the First Intercontinental railroad. These were designed to bring in many more free Europeans to settle out west and ensure all those new territories would be free rather than slave. During, the war, there was a large number of immigrants who did move out West.
All Lincoln needed to do was hold the Union together. With time, free men would do the right thing and vote slavery away.
Many Northerners were racist back then and didn’t want to fight and die in a war to free slaves. So, Lincoln defined the goal as saving the Union in order to defend Democracy rather than save the Union in order to ultimately end slavery. Both were true but the former was more effective in mobilising the North.