Answer: Nixon's goal was not to have a strong federal government, but rather to give more power to the states called New Federalism.
New Federalism: Federalism is a form of government whereby the same territory is controlled by two levels of government. An overarching national government typically governs larger territories, while smaller subdivisions, states, and cities take care of issues that are largely local. Rather than just being controlled by the government itself, Nixon hoped to spread more power throughout the states
How Nixon Worked Toward His Goal:
On October 20, 1972, President Richard Nixon declared an open attempt at reversing the flow of power from the federal government back to the states. In 1972, Nixon signed a bill that incorporated revenue sharing with the states and gave over $30 billion to state and local governments. The State and Local Fiscal Assistance Act of 1972 authorized the federal revenue-sharing (FRS) grants which were given to state and local governments over a period of four years until 1986 under President Reagan.
I know this really isn't an answer but I know Crash Course has a video on it on YouTube.
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