Edit: I wanted to add,
Weren't most of the American colonists revolutionists at that time? If so then did this just add more fuel to the fire, so to speak? It's my understanding that the war started in 1774, but this was published in 1776; why was this regarded as such an important document?
In fact only about one third of the population in the colonies supported the Congress, one third was strongly loyal to the Crown, and one third just wanted to have a pint and wait for this to all blow over. This is a generalization, but makes a good reference point to think about. The same pattern holds true in many revolutions, such as the French, Bolshevik, and Nazi revolutions.
Common Sense summarized the primary arguments in favor of the revolution in a clear and familiar fashion that helped provide a starting point for discussions on the topic that near everyone would be familiar with, due to its immense popularity.