Actually, they did many times. I'll provide one example and let others here add to the list.
Late in the war, Confederate General Jubal Early assaulted the outskirts of Washington DC in an attempt to take the city and the seat of the Union government. He was fought to a standstill at the battle of Monocacy by Union General Lew Wallace, who later wrote the novel Ben Hur. Add to this at least two excursions into northern territory by R. E. Lee, Antietam and Gettysburg.
OK scholars, anymore?
That is NOT what happend here!