While this is not true it is close enough to be a workable model for most people.

"Many even believe that the Federal Reserve is actually an independent entity that “loans” the government the money it needs to pay for stuff not covered by taxation."

The first fallacy is "Independent" the Fed is "Quasi-independent" it does not take direct orders from the Treasury or any other government agency but it is far from politically independent.

The second fallacy is "loans" the government money. It is in fact the lender of last resort should nobody else be willing to buy U.S. government bonds.

So this belief you say many believe is not really so far out of reality.

You say that government spending is what creates money (or as you say currency) but the Fed controls the money supply and can take money out of circulation or put money into circulation as fast or faster than Congress. There are even words that differentiate Congressional action from Fed action.

Congress can put money into the economy with Fiscal Stimulus and take money out of the economy with taxes. The Fed can put money into the economy with Quantitative Easing or Interest rate cuts (Monetary Stimulus) and take money out of the economy with Monetary Tightening (Taper or even reducing it balance sheet) and by raising interest rates.

Yes, the debt ceiling fight is just theater that obfuscates where the real controls lie. The U.S. Congress changing the laws to allow it to spend money without borrowing would only create new money if the Fed did not counter that with interest rate increases or sales of assets from its balance sheet.

What we should be talking about is who we want to control the money supply, Congress or the Fed.

TEK