The problem is that the Confederacy is just living on borrowed time. McClellan had every intention to continue the war (even though many of his supporters were anti-war! Indeed, Clement Vallandigham was made his war minister).
McClellan is not as gifted as Lincoln, this is true, but the war doesn't immediately end.
And the longer term is even harder to consider. The Confederacy had major internal problems; Lincoln had announced the Emancipation Proclamation, and slavery was now working very heavily against the South. It's fair to claim that the CSA would be facing partisan activity throughout the length of their country, something that would worsen throughout the war.
Add in the large number of portions of the CSA that seceded from it and you have Partisan hell. Various Counties and Towns seceded from the CSA as a result of its actions, creating major internal weaknesses that could not possibly help the South. Finally, Slavery is a rich man's luxury and a poor man's burden, particularly in the furnace of the Civil War.
McClellan isn't enough to end the war. Indeed, after the Emancipation Proclamation, no one in Europe really wanted to get involved in the situation. What is likely to happen is a fading of the Confederacy. Grant is going to be able to smash Lee with enough Troops--and McClellan, despite his faults, is going to support the army as much as Lincoln did, if not as competently.
The Confederate States are out of Answers. By 1865, they have no real source of manpower left. While nations in desperate straits sometimes take drastic measures (Drafting Women and Children, Prisoners, etc), the CSA doesn't strike me as willing to make these kinds of sacrifices. Indeed, by 1865, despite still holding onto large sections of territory, the CSA folded.
And these tensions would have intensified as the war continued. Grant is almost certainly going to grind Lee Down. McClellan is a capable administrator and will be able keep the war effort up for the Union. The CSA doesn't have what it takes to hold on to 1868, nor is it internally strong enough to do so. The CSA can not retreat inwards--doing so allows slaves to link up with Union Forces, and believe you me, the slaves were eager to fight.
It seems like the CSA probably folds in 1866-7, rather than 1865. Which is still impressive, but remember: Lee's health is failing. The USA is strangling the CSA's economy. Slaves and poor whites are creating partisan activity behind the lines. And by this point, the CSA is slowly losing pieces of its territory. By this 1864 scenario, the Union would almost certainly have sent an Army though Missouri, and into Arkansas. The Fall of the Mississippi River is an eventuality with Union Naval power.
I guess that there is no real way for the CSA to win, unless the USA cracks first. Which I don't think was likely to happen.