What evidence is there that the Federal government became too powerful in the 1930’s?

"Too powerful" is kind of a relative term, but there is no denying that the federal government moved into the private sector more than ever before thanks to the New Deal. The federal government got involved in industry by banning child labor and creating a minimum wage with the Fair Labor Standards Act. The government also got involved in agriculture through the Agricultural Adjustment Act. This act controlled the supply of farm commodities that could be produced and created price floors. Before this, farmers were at the mercy of the markets. The federal government actively employed people through the Tennessee Valley Authority and the Civilian Conservation Corps. The government also created a pension system through Social Security. Government also regulated the banking and investment system through the FDIC and the Securities and Exchange Commission.
Franklin Roosevelt ran into some controversy with his New Deal as the Supreme Court tried to strike down some of his legislation. His court-packing scheme was unpopular with the public and helped end the New Deal, thus proving that the people did not want to give the federal government what they regarded as excess power. The New Deal did put the federal government more in the lives of the public than ever before and helped open the door for further legislation such as Medicaid. Calving Coolidge once bragged that it would take the average person some time to notice if the federal government ceased to exist, due to its small impact on their lives. Franklin Roosevelt made the federal government a prominent player in the lives of Americans. It is hard to say whether this is for good or ill, as it all depends on your political leanings.