From 1934 to 2015 the mean difference between the national debt and commercial bank assets has been as follows: National Debt = 0.94 x Commercial Bank Assets. There is a simplistic narrative of the national debt that goes as follows. The government spends into the economy and then removes some of the spent money and then spends more, etc and the amount the government does not take from the economy is equal to the debt. This simplistic narrative does not include the complexities of a central bank, an endogenous money supply system, etc. Is it possible that the narrative is true but the system enables commercial banks to "capture" the money as their assets?
A fundamental principle of accounting is that the liabilities of one party are the assets of another. National debt is simply the amount owed by the federal government – that is, its liabilities. Some other party must hold these as assets, but it need not be banks: households, other financial intermediaries (such as insurance companies and pension funds), and foreign governments all hold substantial amounts of U.S. government debt as assets. Likewise, banks can hold claims on debt issued by entities other than the federal government – for example, residential mortgages or corporate bonds. In short, there is no reason for a tight mapping between government debt and bank assets, though it is not surprising that the two are positively related in the long run. For a comprehensive account of the financial positions of various entities in the U.S., please see the Financial Accounts of the United States (http://www.federalreserve.gov/releases/z1/current/z1.pdf).