Federal Debt Emergency Control Act of 2021 This bill establishes various budget enforcement procedures to address the federal debt. The procedures established by the bill take effect during any fiscal year that follows a fiscal year in which the amount of federal debt exceeded the gross domestic product (GDP) for that fiscal year. During such a period, the bill rescinds unobligated balances of stimulus spending that was provided in specified bills that addressed the impact of COVID-19, establishes a point of order against legislation that increases spending, and requires Congress to consider certain deficit reduction measures using specified expedited legislative procedures. The expedited legislative procedures must be used for legislation that (1) would reduce the deficit by at least 5% during the 10-fiscal-year period following the current fiscal year, and (2) does not increase the rate of any federal tax or increase any fee paid to the federal government.