Do you think the Civil War would have happened if Abraham Lincoln had not been elected President?
Counterfactual history is always hard, and professional historians try to stay away from wondering "what if." That said, it is fun to ponder what would happen if Lincoln was not elected. It is entirely possible; after all, he only received 49% of the popular vote. A Lincoln defeat would have left the Democrats in charge of the White House, and Stephen Douglas would not have wanted to alienate Congress by doing anything to end slavery. The Lower South would not have seceded--this would have taken away the immediate cause of the war.
The next question now should be this: how would America look in the era between 1861 and 1864? The nation was already showing signs of strain: John Brown's raid in 1859 and "Bleeding Kansas" already proved that people were ready to shed blood over slavery. The Republicans would have had more power in 1864 as the North gained more immigrants than the South and would have probably won that election. Lincoln was not even the party's first choice, and a ticket with a Radical Republican such as Edwin Stanton would definitely lead to war, this time with the border states seceding as well to maintain their slavery rights. To answer your question, war would probably be inevitable when a Republican managed to take the White House due to the growth of the North.