What does each level of government face as challenges in the developing relationships between local, state, and federal government?

The most fundamental challenge in the developing relationship between different levels of government in the United States is the evolving definition and view of federalism.
The relationship between federal governmental authority and responsibility on one hand, and that of the states and the local governments they created on the other, was defined by the concept of dual federalism in the early history of the United States. Dual federalism saw each component's duties effectively placed into self-contained silos.
Since the Civil War, but more intently since the New Deal, this relationship has evolved into what has been called cooperative federalism. In cooperative federalism, the different levels of government do not have duties that exist independent of other levels but, instead, overlap. The challenges this presents are two-fold.
First, cooperative federalism tends to favor the federal government over those of the states and localities. That is, the responsibilities of the federal government are more likely to spill into areas traditionally reserved for the states and localities than visa versa. This has been derisively called "one-way cooperative federalism."
Second, cooperative federalism does not have clearly defined limits and is in a state of continuous evolution, creating the need for continuous case law creation to determine its boundaries.
http://arizonastatelawjournal.org/wp-content/uploads/2017/11/Kincaid_Pub.pdf