I just don't see it; even with a stalemate in North Georgia, the writing is on the wall for the rebellion, and - as it is - the US has already liberated West Virginia, Tennessee, much of Virginia, parts of the coastal Carolinas and Georgia and Florida, parts of the Gulf Coast from Alabama to Lousiana, and much of the interior of Lousiana, Mississippi, and Arkansas, along with (in 1861-62) securing Maryland, Kentucky, Missouri, and the Indian and New Mexico territories. See below:
http://www.history.army.mil/html/bookshelves/resmat/civil_war/Maps/1CW-1861-1865.pdf
I mean, what's left to make peace with?
The reality on the ground is another reason why I think the whole "rebels get a political win through a Fabian strategy in 1864" concept is unrealistic; the rebellion was defeated militarily in 1862-1863 - the last two years of the war was (to be blunt about it) mopping up...
The rebels had to be beaten down to secure the peace (not unlike the Axis in 1945) but the realities were clear.
On edit: if you want a tradition of intervention in the US economy by the federal government beginning in the Nineteenth Century and moving beyond the (historical) range as a matter of policy that is accepted by both major parties, there are ways to get there that do not require a rebel victory in the Civil War...
Prolonged European - read French - intervention in the Western Hemisphere after 1865 could lay the groundwork for it; the Russians not selling Alaska, the British being stupidly provocative in BNA and not coming to terms over the
Alabama Claims, the Spanish continuing to fight on Hispaniola or actually sending an expeditionary force against Chile and Peru ...
The Spanish actually doing something really stupid like trying to intervene in Mexico alongside the French could lead to active US hostilities in the late 1860s against Spain, which is close enough to the Civil War that the naval issues exposed by the
Virginius affair have yet to arise; as it was, the federal government was pretty deeply involved in the economy from 1861-65, and certainly was involved in parts of it - the transcontinental railroad and the Homestead and Land Colleges acts in the 1860s, the impetus toward a modern iron and steel and shipbuilding industry that started in the early 1880s; there was a lot going on, even when it tends to get submerged by the Gilded Age frame.
Best,