US Grant dies from his first fall off his horse shortly before the Battle of Shiloh due to the soft ground that saved him being rather harder. Without Grant the US Army under Don Carlos Buell wins an Antietam-style victory near Corinth, but the Confederacy is able to fight the war without a sufficiently ruthless and aggressive general in the West able to follow these victories up.
As a result, with the Union offensives in Virginia never gaining anything, and with the absence of Sherman and a buttload of Buells and McClellan-types who win battles but never campaigns or true victories over Confederate armies, the US population elects Horatio Seymour in 1864, who signs the Treaty of Baltimore with the Confederacy, recognizing it as the 11 1861 states plus the Indian territory. The election of Seymour is due to a repeated pattern where US troops would go on the offensive with superior numbers, only to have to detach so many troops to occupy territory that Confederate soldiers achieved local superiority of numbers and prevented the Union from ever getting too far past Kentucky and Missouri. Too, Confederate guerrilla and partisan war policies in the ATL are blown quite out of proportion to the real results of the war, which showed that Union troops were able easily to suppress them by mid-1863. Lee's strategy's potential damage to the Southern cause is limited because the Union strategic victories in the West never mollify his repeated victories over McClellan and his similar type of officers, who in turn squander the largest army that had yet been raised in North America. In the ATL this is used to subvert the idea that Steamroller strategies are viable, and is used as an example of why Russia loses the Russo-Japanese War.
No Grant or Sherman, the Union has a great deal of leaders who prefer the Soft War policy to the Hard War policy, and no examples of successful generalship with a great deal of examples of crapsack generals against Confederates more than able to exploit their victories. CS victory is attributed due to having had the foresight to outlast the USA in a war of wills and to the inability of any US Generals to follow up Grant's victories at Forts Henry and Donelson with an offensive that might not merely have defeated the pivotal Pittsburg Landing Battle, but outright stopped Confederate power near the Mississippi as a threat to the Union.
Confederate histories hail Joe Johnston and his Fabian Strategy as the key to victory, and there's a subtle undertone that had General Lee ever faced a competent opponent he could easily have ruined the CSA by his victories. Foreign observers attribute the Confederate victory to the Union's folly in trying to invade a region the size of Russia in Europe and conquer it without any degree of foresight and with a political leadership handicapped by damnfool generals. The Union Anaconda Plan in the ATL becomes a source of AH Fodder, as does the question of what Grant might have done had he been in charge of defeating Johnston's counteroffensive, not Buell.