During the American Revolution and in its immediate aftermath, the former colonies were organized under the Articles of Confederation, which did indeed give most of the power to state governments rather than a central federal government. This caused a lot of problems, chief of which was that the federal government could not compel the state governments to give them money to pay the soldiers who had fought in the war. The problems with the Articles of Confederation prompted the drafting and ratification of the US Constitution, which created the United States of America as we know it today, with a federal government sharing power with state governments (although nowadays, the federal government definitely has the lion's share of the power).