The secret is not simply throwing money at a problem. FDR's New Deal, JFK's New Frontier, and LBJ's Great Society never relied simply on throwing money at a problem. Their secret was to get people to throw themselves at the problem and then--once they knew what the problem was--ask for the money to fix it.
The "dollar a year men," Civilian Construction Corps, Works Project Administration, the Peace Corps, VISTA, Project Head Start: all of these relied on getting people involved in solving the problem, not simply giving money to often corrupt local governments or private corporations.
I believe that a strong case can be made that the efficiency of many domestic programs (particularly those initiated under JFK and LBJ), were hampered (especially in the area of education), when the Federal government under President Nixon began handing out block grants (for example to state education departments and local school systems), rather than the area specific funding that had been the practice before. Monies disappeared into administrators' "pet projects," rather than new text and library books, art and music supplies, etc. The number of administrators in schools and school districts grew; the number of teachers per student shrank.
Democracy is a form of government that requires a "hands-on" approach, at every juncture, if it is to work correctly. Unfortunately, Americans have fallen out of the habit of good citizenship, of making certain that their elected representatives truly represent them, and that their "civil servants," remember to be civil to the public, while providing that selfsame public, service. Americans must at the same time remember that their representatives and civil servants are there to serve the American public as a whole, not every American's desire individually. We should always receive an answer from our government, even if sometimes that answer has to be "No."
No, what must be done does not involve dismantling of Big Government, certainly not in its early stages. Big Government will be required to battle the true villain of this piece, what Theodore Roosevelt called Big Business.
Big Business--i.e. the giant multinational corporation--hates democracy, or for that matter any form of republican government where there is not some form of an oligarchy or aristocracy established with special rights above and beyond those of most citizens. It is this privileged class of oligarchs who actually run the government, solely for their own benefit.
Big Business only wants enough education for the lower and middle classes to enable them to work in the giant corporation's factories, mines, stores, and offices, at slightly more than subsistence wages. Big Business does not want its workers to have enough education so that they might start demanding better pay, benefits, and working conditions for themselves or their fellow workers.
Big Business hates competition, in part because they want to pick and choose among the best qualified workers for themselves, rather than risk having to compete for their services, and coincidentally pay a higher wages and benefits for those services. Big Business also hates competition because it reduces their profits at the end of a quarter, profits they are certain by right belong to them.