There's no perfect answer to this question (even the question acknowledges this problem). In my opinion, the U.S. was put on a path to Civil War the very moment the U.S. Constitution was signed. The Constitution brought a bunch of colonies into a union together, even though some of those colonies relied heavily on slavery and believed that slavery was morally defensible, while others did not rely on slavery and believed that slavery was a terrible thing. It was only a matter of time before the debate over slavery turned into a violent clash over slavery.
Answer: The Declaration of Independence provides a foundation for the concept of popular sovereignty, the idea that the government exists to serve the people, who elect representatives to express their will.