If Shelby Foote is to be trusted, two things kept the Union from a quick victory:
1) General George McClellan, at the head of the Army of the Potomac. The guy was incompetent on the battlefield; you could bluff him out of attacking by (for example) making your troops march in a big circle to give the illusion of an unending line of soldiers. That actually happened; advisors of Lincoln's debated whether McClellan was losing the war on purpose or was he really that stupid. Later McClellan ran against Lincoln in 1864, on an anti-war platform. Basically, McClellan was Starscream.
2) It took a while to figure out that Ulysses S Grant was the right guy to put in charge of the Union armies.
Don't let the South hear you say that. Next thing you know, you'll get all the Southern manchildren raised on daddy's knee thinking Lincoln was Megatron.
I've read many Civil War journals in my day, and most seem to confirm that once the North's trio of trained murder-horses made it over the bridge, that was game over
I'll ask my friend the history teacher about "trained murder horses" and see if he'll agree to show this video in class during the "Civil War" section of class.
He already has a lesson based off of the song "James K. Polk".
There's an interesting little civil war game called AGEOD's Civil War. All of your commanders have both a strategy rating and political rating. The strategy rating reflects how effective they are at command, while the political rating simply reflects how well connected they are to receive cushy jobs. Promoting able commanders over those with better political connections results in loss of national morale and points as they raise a shit storm back in Washington.
Naturally McClellan is your worst commander but has an astronomical political rating. A big part of the game is picking the right time to fire McClellan and replace him with someone unpopular like Grant or Sherman and weathering the massive point hit penalty.
Or some people figured out you can cheat the system and just give McClellan a ghost command with a bare bones army patrolling New England while Grant fights the real war.