“We had a balanced budget AND surplus (actual debt reduction) under President Eisenhower, well after the establishment of the Federal Reserve.”
That occurred for only one year, 1956.
The chronic postwar increase in debt and foreign assistance led to the Triffin dilemma, the first sign that the gold linked dollar was in trouble. The first public sign of the problem was the abandonment of silver coinage in the early 60s.
We are going back to the era of the continentals. That was the reason we went to a gold standard. It may have also been why the Constitution calls for gold and silver as a repayment for debts, but omitted the words emit bills of credit as contained in the inferior Articles of Confederation.
The reason we're in a big debt fiasco is because of entitlement spending - social spending. Every Federal dollar of revenue received right now, from all sources, just barely covers spending on Social Security, Medicare, Medicaid, and income security (unemployment, welfare, food stamps, subsidized housing). We run the rest of the Government - DOD, DHS, HUD, DOEs, FDA, DOA, FBI, CIA, etc. - on 100% borrowed money.
Having a gold standard, or eliminating the Fed would not stop the Government from borrowing - we have a VERY long history of national debt even when on the gold standard. The problem isn't how the debt is denominated (gold or faith-and-trust in the US); it's that Congress and the President can simply raise more debt by legislative action. And they've been doing so - and using it as payola to win political favor - for the better part of 100 years, with the last 50 really showing it the worst (starting with LBJ's buy of racial minorities in the 60s).