As I understand your question, your main faction controls all of DC, and has built this wall around the governmental 'hub'. They also control some of the surrounding states, so have a fair decent sized buffer around there wall (My knowledge of American geography isnt great so I probably don't fully appreciate the entire lay of the land).
I'm assuming here that this wall is several miles long based on google maps. That would take a lot of building resources and manpower that could be used to kuch greater effect elsewhere (like farming, constructing defences on the frontiers of their territory etc).
While it would be a substantial obstacle for a post-apocalyptic military, provided Virginia has combat engineers (or even just enough artillery), they would be able to make an entry point eventually. The defenders need to protect the entire perimeter, the attackers only need to be successful in a few points.
More than anything else, however, if Virginia manages to push Columbia back to the wall they will have already lost, whether or not Virginia is actually able to breach it. Without any farmland to sustain them and no allied forces that could help them break out they would cease to be any genuine threat, and could just besiege the capital until their surrender. It would make more sense for Columbia to focus on defending further afield.