The national government, the federal government, has way more control than people would have thought. Look at the educational system. Education used to be local. Now the federal government has gotten involved in the last decade, starting seriously with No Child Left Behind, and not for the better.
We can call our present system a system of cooperative federalism rather than dual federalism because the national government is much more involved in state affairs than it used to be. The federal government now uses the money that it gives to the states to have control over policy areas that used to be reserved for the states. So, for example, the federal government requires the states to go along with the No Child Left Behind law. It does this by saying that states can only get aid for education from the federal government if they follow that law. Thus, the federal government is forcing its way into areas that used to be the province of the state.