Saphroneth
Banned
The CSA wasn't trying to take a major Northern city, at least I don't think so. They were trying to make the North consider the price too high.The western part wasn't though and that could have been pushed back as could have been the Homestead Act. It also doesn't change the fact the quickest way to end the draft riots up north is to have Southern soldiers wreck havoc there. The stronger party can get away with it , the weaker one will merely piss off the stronger one. Also the South simply didn't have the logistical capacity to take a major Northern city and never even tried.
This is doable - and, in fact, treating CSA soldiers as treasonous and executing their leaders in job lots is the best possible way for the CSA to end up independent. It's exactly how to get a vicious guerilla war and for the Union to lose all legitimacy in the eyes of the South.
Of course, it'd pretty much tear the CSA to shreds - think, say, Afghanistan during the Soviet invasion.
Anyway, as for the transcontinental railroad - yes, the western end can be pushed back. But my point is basically that it was already the case that the Union couldn't spare enough manpower to do all the things they wanted to do, so some tradeoffs are going to quickly become more and more necessary.
Example - they were still producing a food surplus, but if they take too many more men from the fields that will reverse itself and the economic situation of the Union will become worse. If they do what OTL Britain in WW2 did and rely on foreign produced munitions to a greater degree (by moving people from factories to the front) then, again, their economic situation gets worse.