The issue is probably more problematic than Snake originally stated. Even in a "Lee destroys McClellan" scenario, the Union controls most of Tennessee, most of Arkansas, and the entire Mississippi River in the 1862-1863 timeline. And of course, western Virginia.
A "super Perryville" presents some problems, but unless the war immediately ends, the Union has plenty of time to recover its position in Kentucky and eastern Tennessee. Recovering from this may prevent it from expanding elsewhere in the west, but I think the Union could use the time it has during the mediate peace talks. Because from that point, the issue is no longer will the CSA become independent - it will be because Union morale is no longer sufficient to force the entirety to return - but how much of the territory of the seceded states can be retained in the final peace settlement. BOTH sides need to be realistic and accept what they can hold, versus what they ideally prefer. By the time the Europeans begin the peace process, the Union can recover in KY and still keep its western gains, even if it's recognized that Virginia can't be taken.
By summer 1863, almost the entirety of those areas are in Union hands. Even in a mediated peace, the US can likely keep those four states (WV, TN, AR, LA) since WV, TN and AR have substantial populations loyal to the Union, and control of the Mississippi River is essential to the US. Lincoln can't give that up - it's too important. Texas is cut off from the rest of the Confederacy, but that may not be a big stumbling block towards peace. Texas might be just as happy to be detached or even use it as a chance to become its own nation.
If McClellan botches Antietam, there is a huge issue with whether the Emancipation Proclamation is ever issued. But if there is, there is potentially a huge mass of freed slaves to possibly incorporate into the Union. I doubt any European mediator would insist on their return to slavery as a condition for peace.
In any case, I don't see slavery lasting very long whether we have only a Border State slavery situation (Snake's scenario) or an expanded Union scenario (where the Union keeps what gains it won in the battlefield). Slavery is banned from the territories obviously. Among the states, some form of compensated emancipation may take place, perhaps combined with a deferred emanicpation with future generations of blacks born free, or a rolling automatic emancipation in the future. Without the Deep South fire eaters, the position is untenable in the long run. By 1890, slavery is gone.
Even if the Republican Party is discredited for its loss in the war, the free soilers will be back in yet another party.
Of course, another issue is what will the US do with all of those fugitive slaves fleeing the CSA and crossing the border into the USA?
