The COVID-19 outbreak has caused uncertainty risk surges, increased sustainable supply chain vulnerabilities, and challenges to sustainable supply chain resilience (SSCR) management. Therefore, improving SSCR is necessary to alleviate vulnerabilities, and SSCR management must generate large capital investments. However, the economic downturn brought about by the COVID-19 epidemic has made some companies have limited budgets that can be used to improve SSCR. Therefore, the design of resilience solutions needs to fully consider the constraints of budgetary costs. Most of the existing related literature only discusses optimal resilience solutions under certain cost constraints, so such resilience solutions cannot be applied to most enterprises. In this study, we set the cost constraint as a variable quantity, using resilience efficiency and customer satisfaction as indicators, to determine the changing laws of optimal resilience strategies when cost constraints change. These rules can be applied to enterprises with different budgeted costs. Our findings suggest that companies should prioritize sacrificing resilience measures (RMs) related to adaptive capacity when budget costs gradually decline, and RMs related to absorptive capacity are indispensable at all budget levels. Furthermore, the pursuit of environmental and social sustainability cannot be abandoned, no matter how limited the flexible budget may be.