First, I'll provide some background before I more directly answer your question. The United States has a federalist system of government. In our federalist system exists a very delicate balance of power between state and federal government. There are delegated power belonging to the federal government, reserved powers belonging to the states, and concurrent powers shared between the two entities. The Necessary and Proper Clause has expanded the role of the federal government in many ways allowing the federal government to stretch their delegated powers if need be to properly execute those (delegated) powers. On the other hand, the 10th Amendment assures that any power not delegated to the federal government are reserved powers for the states. As a result, we have historically seen the ebb and flow between state and federal power. Often, this shifting of power is described as a pendulum swinging between the two levels of government.
The Great Depression and WWII are two events that caused the pendulum to swing in favor of the federal government. The magnitude of the Great Depression left citizens and state governments looking to the federal government for relief. Typically, local and state governments would have been responsible for providing adequate relief but considering the high unemployment rate, homelessness, bank failures, and the abundance of other issues, the local and state governments' resources were exhausted leaving citizens looking for more support. Though FDR was initially opposed to expanding the power of the federal government, when he ran for office he recognize the need for federal aid and promised the American people swift action to overcome the economic and social woes. FDR delivered on his promise when he instated the New Deal which created numerous agencies and federal works programs to begin to aid with the recovery of the economy. Additionally, FDR's fireside chats allowed the president to use the bully pulpit to persuade Americans he was a strong leader and to restore confidence in the American people so he could continue to pave the way to economic recovery. FDR's First Hundred Days were marked by the continued expansion of the federal government. As the federal government (specifically the executive branch) increased in size and scope, states and citizens alike began to rely on the federal government. Unlike other times in history, the Great Depression permanently increased the size and scope of the federal government (specifically the executive branch) as the reliance on many of the new projects and programs created during this time never dissipated (FDIC, Wagner Act, and Social Security are just a few examples). Though the pendulum has shifted back to the states, this is known as devolution, the size and scope of the federal government is generally much larger as a result of the Great Depression.
Hope you found this helpful!