If a city gets the Regional Decision Card to gain a telegraph, then it may become Rich. This provides much more supply. Other players have encountered a seemingly unlimited supply in their capital. I tried to sever VA from the rest of the CSA once by taking the railhead at Garysburg and destroying all the depots in that state, but this wasn't a viable strategy.
I am usually capable of mustering an Army with two Corps of 12k power for Grant. I suppose a determined offensive might eventually succeed. IIRC, the terrain is forest, which limits artillery use. However, if the defenders can be driven into the city, the defenses have a garrison limit that cause a large force to suffer from overcrowding.
I'm the 51st shade of gray. Eat, pray, Charge!