Who is to say that the American people wouldn't get foreign support? Chances are that if the people are upset enough to start a war, that foreign nations would have thin ties to the Govt. Already?
Foreign support would tip the scales completely.
Also, if the revolutionaries are well organized, they would be smart enough not to go toe to toe with the government in a "gun fight."
I would imagine a lot of espionage and public propaganda. Also you forget that our military is made up of Americans. If an American soldier was ordered to fire on their people, they may desert. Not all of them would, but it would be a significant factor. This is especially true if the majority of the people were involved in the civil war.
You might ask why I have outlined this as a war against the govt.? Well, the first thing the govt. May do in a civil war is take a side and declare the "rebels" as terrorists.
No I do not think it could be solved like last time as we have a lot more powerful war equipment then when they had there civil war. Also I think that the politics would intervene a lot more and make it worse. I just think it was a lot more simple then than it is now.
It really makes no sense why we would go to another civil war. It's not like back then with the Confederate States and the Union, we find ways to solve stuff without violence in politics, and if we disagree on an issue (we do a lot) we usually put it aside. I mean, all the parties have a chance to have a President.
While it's not impossible, I think it is unlikely because so much of our military's assets are federalized. For instance, our nuclear warheads would not be able to be fired because they would require the launch codes of a president on the other side of the lines. Any attempt at launch would be shot down by our own missile defense. Were it to be solely conventional, too much of our military is spread across the globe. No telling if they would even be able to mobilize.
The only scenario where I could see the potential for a modern era Civil War is if the federal government were to fall for some reason. In this scenario, I suspect that you would see the liberal states and the conservative states both attempt a grab for power. Based on this concept, I feel as though the gun-weilding conservatives would likely be at an advantage over the liberal groups that, generally speaking, don't advocate violence. When you take into account that large swaths of the military come from small-town and conservative upbringing, the possibility of a modern era Civil War is probably best kept within the Marvel movies.
Currently their isn't a single issue that has polarized the nation so much that a group of states would attempt to succeed from the union (like slavery). If a civil war did break out, it would be a one sided fight. The amount of conventional firepower that the US Military has is far superior to anything the states could muster together. The only way I can see a civil war lasting as long as the first one would be if Generals and Admirals from the US military succeeded with the separatist states, taking their men, weaponry, and supplies with them.
The likelihood that another Civil War would end up the same way is improbable. The outcome of another Civil War would probably be far more bloodier, and far less of a chance of having a president with ideals such as the ones of Abraham Lincoln. Having all that repeat itself once again, probably ain't gonna happen.