***** NOT A TEACHER *****
Hello, Badol:
I agree with you: that is a very difficult sentence for learners (and even some native speakers) to understand.
You have to realize that here in the United States, the Civil War (1861 - 1865) is a VERY sensitive subject. That is, it can make many people VERY angry. In fact, some people prefer to call it the War Between the States.
"Neo-secessionist account" means something like: a new or different way in 2014 to look at the history of the Civil War. Many (most?) Americans feel that the "neo-secessionist account" is wrong.
(By the way, "secessionist" comes from the verb "secede" (leave). As you probably know, the Southern states wanted to leave the United States of America.)
If a man falls down, is it a good idea for all the people near him to jump on his body? Of course, not. According to the sentence, it seems that MANY people have criticized Mr. DeMint's opinion about the Civil War, so if one continues to criticize it anymore, it would look as if one were piling it on. That is, Mr. DeMint has been criticized enough. If one continued to criticize him, other people might say, "Hey! Isn't it time to stop criticizing him? Haven't enough people already criticized him? If you continue to criticize him, people will start to feel sorry for Mr. DeMint, and they may then start to believe his opinion."
