The issue is that Lincoln himself said that the Constitution was a "compact" between states. The beef arose because the southern states felt that the compact was not being up held and that the federal government was not acting as a good administrator of the compact.
Under compact agreements if certain parties are found to not be upholding their end the others involved are free to leave. Some at the time called the constitution a "contract." If a contract is not fairly administered or certain parties are found in breach the damaged parties can be let out of the contract. What Lincoln was doing by refusing to allow the southern states to leave the Union was an astonishingly new doctorine legally and politically.
The issue had been brewing for over forty years. Concessions had been made on all sides. It is long and complicated. My only answer to what would have happened, we will never know. Any speculation is pure conjecture from all involved. Slavery would have eventually ended I believe. I also believe that the CSA would have either become a third world country or came back to the Union over time.
I believe allowing it to happened would have shown much more respect for the founding ideals of our country than Lincoln's war or presidency ever did. I also believe it would have stopped a lot of our current problems. It would have avoided setting a prescedent that basically said, "screw the Constitution, the Bill of Rights, and the Decleration of Independence."
When in the course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
The CSA did that. Whether or not Lincoln agreed with their reasons is not important. How we feel about it is unimportant.
That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.
That is what the CSA were trying to do peacefully. Whether or not we agree with them they were following the basic principles that the founders cited in declaring freedom.
I could go on and on, but ATS and time limit the amount of typing I can accomplish. I do not agree with the positions of the CSA. However, I do believe they had the right to secceede. If Lincoln had allowed it, many things could have happened. The one definite is that it would have shown respect for the principles that formed the nation and the rule of law.

