What was the greatest concern of the opponents to the constitution?

The greatest complaint was that the Constitution created a federal level of government that had the potential to become completely supreme over the individual states. The Constitution itself states that appropriate Federal Laws and actions constitute the supreme law of the land and that states are bound to abide by them. At that time, states considered themselves virtually sovereign as against any other state or federal government. To placate concerns of such states, the Constitution was written in such a way that it gave the federal government only specific enumerated powers, reserving to the states all other powers not expressly given to Congress. This was supposed to allow states to still conduct their own internal affairs as they saw fit without interference from what might become an all-powerful federal government.