Pandemic Regulatory Cost Relief Act of 2020 This bill prohibits the promulgation of rules during and following the COVID-19 (i.e., coronavirus disease 2019) public health emergency that have been estimated to increase the compliance costs of the regulated entities unless such increase is offset by a corresponding nullification of rules or the Office of Management and Budget determines that no such offset is available and that the rule is necessary to protect the public against the pandemic or to protect national security.