Pickensburg
Actually, neither of the two regiments named were real, nor was there ever a Battle of Pickensburg during the Civil War. It seems that this fictional battle took place early in the war (there is a reference later on to the year 1861), and that the casualties (at least on the Union side) were heavy They said that death-rate couldnt be beaten
about one in five of us got out safe. In these respects, the fictional battle at Pickensburg would have been not unlike the first major Civil War battle, the First Battle of Bull Run, fought in Virginia in July of 1861, where approximately 3,000 of 30,000 Union troops were killed, wounded, captured, or went missing. If Howells based his fictional Pickensburg on an actual early-war battle, it would most likely have been the First Battle of Bull Run.

First Battle of Bull Run, 1861 (photo: www.usa-civil-war.com)
The kind of war-time heroism discussed in this scene would no doubt have been found in abundance in this particular battle, on both sides of the conflict. It was at First Bull Run that Confederate General Thomas Stonewall Jackson received his famous nickname, when his troops observed his fearless stance and unshakable position There stands Jackson like a stonewall.