I agree with your conclusion, but there are some significant flaws in your argument. The money supply is much larger than the amount directly spent by the government thanks to fractional-reserve banking and other forms of leveraged finance. These essentially act as multipliers of the portion of the money supply generated by direct government spending.

A spectacular illustration of the importance of this multiplier is the crash of 1929 and the depression which followed. Investors systematically lost confidence in the value of their investments and thus began calling in loans which over-leveraged borrowers could not repay with cash on hand, so they sold off assets at a loss to cover their obligations, decreasing market values, making other investors over-leveraged, who sold off assets, and so on through a feedback loop that ended up contracting the money supply by 30% between 1929 and 1933. FDR’s administration used massive social welfare and public works programs (direct government spending) to re-expand the money supply.