The question is a bit contrafactual, which means it is hard to answer solidly on historical basis. Maybe we should recount what factors were not strong enough for reaching the negotiated settlement.

• Inner opposition to the war in the beginnings. The population of the USA was not really keen on shooting on what was considered the other half of the country for 80 years. There was a strong sentiment of negotiating the peacful separation in the hope of a future reintegration. That idea was held by people like Robert Anderson (the commander of Fort Sumter), Ulysses S. Grant or George G. Meade at some point of their life. The US Army officer choir was not really keen on killing officers, colleagues, friends and sometimes relatives whom they fought together, lived together, struggled or thrived together with. So it took a big, concentrated effort to start the war for starters. But at the end of the day the failure of moderation happened. It took silencing about 300 newspapers, locking up 14-30 thousand citizens who were against the war, the suspension of the Habeas Corpus, deportation of an elected Congressman.
• Continuing resistance to the conduct of the war. Later on there always was a lingering suspicion that the Army of the Potomac does not really want to fight the Army of Northern Virginia until the complete destruction, being full of conservative officers who looked for the negotiated settlement of the war. The most known of them were Major General George B. McClellan, former general in chief and commander of the Army of the Potomac and Major General George G. Meade commander of the Army of the Potomac. They were both suspected to be little less than traitors by the Republican Party politicians who were mainly radicals and therefor also strongly pro-war minded. Both were investigated by the United States Congress Joint Committee on the Conduct of the War which were dominated by radical Republicans, who tried to remove them from command. For example regarding why the Army of the Potomac did not try to finish off Lee's army after the battle of Antietam (Sept. 17, 1862) George S. Maharay (and I'm sure metric tonnes of other works mention it too) wrote in the The Ever-Changing Leaders and Organization of the Army of the Potomac p. 63: ’Major John Key, a member of Halleck's staff had an answer for the inaction on the eighteenth. Key was the brother of Colonel Key of McClellan's staff; the officer who had talked about settlement of the conflict with Confederate General Howell Cobb during the Peninsula Campaign. Major Key reported a conspiracy theory, one that Lincoln chose not to ignore. Major Key told the judge advocate of the War Deaprtment taht the pursuit and destruction of the Rebel army "was not the game." He continued, "the object [of the game] is that neither army shall get much advantage of the other, that both shall be kept in the field till they are exhauseted, when we will make a compromise and save slavery." Upon hearing this, Lincoln personally interviewed Major Key on the September 27. And when Major Key confirmed his remarks, Lincoln dismissed him from service, and said that he acted "because I found it was staff talk and I wanted an example."'
• Military victory of the Confederacy. There was no hope at all for that but as many-many historias (like Gary Gallagher) have pointed out a draw would have been enough for the Confederacy. If they had managed only to exist on until they could have been disregarded no more, they would have won. Were there any chance of the draw? Grant wrote in his memoires that if the Confederacy had held out for another year the northern population would have probably abandoned the war effort and made peace. The margin for military errors were small to begin with and despite the Confederacy made heroic efforts to prop itself up for waging this terrible war, it proved to be insufficent. Were there any signs of the exhaustion of the Union? Yes, there were, the desertion of the soldiers, the population moving to Canada to escape the war, the growing dissatisfaction with the growing casualties. But it all was just not enough.
• Political fall of the hawkish factions. The election of 1864 looked very promising for the Democrats until August or September of 1864. The sacking of Lincoln was more or less sure because of the hugely demoralizing casualities coming from the Eastern Theater of the war. The Republican party did not want to nominate Lincoln at all; instead they tried to line up behind John C. Frémont as a radical candidate. Grant was considered for a while as nominee until he shut down the speculations first by supporting Lincoln then by gaining the epithet „the Butcher” with his conduct of the war int he Overland Campaign. So the Lincoln-supporters were actually forced to create a National Union party ticket joined by some War Democrats. As the War Democrats supported Lincoln, the Democratic Party platform would neccessarily be a peace platform and nominated the still immensly popular McClellan. McClellan could not give a comprehensive explanation how can he still be pro-war if the party stands up for peace buti t all would not have been enough if William T. Sherman had not taken Atlanta in September and the radical Republicans had not abandoned Frémont in fear of McClellan’s predictable win. Lincoln was so sure of his demise that on August 23 he prepared the enigmatical cabinet memorandum: „This morning, as for some days past, it seems exceedingly probable that this Administration will not be re-elected. Then it will be my duty to so co-operate with the President elect, as to save the Union between the election and the inauguration; as he will have secured his election on such ground that he cannot possibly save it afterward.” see Allen Carl Guelzo’s speech at the Sacred Trust Talks in 2014.
• Coup d’État. We don’t have too much about this possibility, but we know that McClellan vented out some frustration in his letters he wrote to her wife. One of them contains remarks about ’taking my boys to Washington to check on what is going on there’. On another account he held conversations with three other generals of the Army of the Potomac at dinner, when he mentioned that some others encouraged him to take decisive action with the help of his loyal friends. That was after the Emancipation Proclamation was announced which made the conservative McClellan furious. See again Maharay.