Actually, the 50's and 60's should not be viewed as times of small government, though compared to today they are.
Big Government started in earnest under Franklin Roosevelt as his response to the Great Depression. It mobilized and fought World War 2 under the overall direction George Marshall, who later became the architect of the Marshall Plan to rebuild Europe. The most famous American general of WW2 was Dwight Eisenhower, more an administrative-political general than a war-fighter. Since WW2 resulted not in a pacific state of affairs but rather in the Cold War against the Soviet Union, as President starting in 1953 Eisenhower, despite the warnings late in his term about the military-industrial complex, brought this Big Government administrator point of view to Washington DC, as an example initiating the modern US highway and freeway system.
The '60's saw the introduction of The War On Poverty and The Great Society under Lyndon Johnson, while as a response to growing (and justified) racial discontent the Civil Rights movement was born, and a bureaucracy to put the resources of the government to work aggressively addressing it.
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