The federal government was never intended to administer services or benefits directly to all US citizens. The US Constitution enumerates a very limited set of federal powers: defense, foreign policy and regulation of interstate commerce, none of which concerns the average citizen day to day. It was intended for state and local governments to directly serve the people in almost all circumstances.
The New Deal was a terrible imposition of big government on the country and we're dealing with the cascade of problems and constitutional issues to this day, SSNs being a very visible example.