The Pioneering Antimicrobial Subscriptions To End Up surging Resistance Act of 2020 or The PASTEUR Act This bill authorizes the Department of Health and Human Services (HHS) to enter into subscription contracts for critical-need antimicrobial drugs, provides $11 billion in appropriations for activities under the bill, and contains other related provisions. A manufacturer of a Food and Drug Administration-approved antimicrobial drug may apply to HHS to have the drug designated as a critical-need antimicrobial, and HHS may enter into a subscription contract for such a critical-need antimicrobial. The bill imposes certain requirements related to such contracts, including a mechanism to lower payments under the contract in certain instances to limit the manufacturer's revenue from the drug. Furthermore, HHS and the Centers for Disease Control and Prevention shall award grants to support efforts to encourage the appropriate use of antimicrobial drugs and efforts to combat antimicrobial resistance. HHS shall also establish a Committee on Critical Need Antimicrobials. The committee shall develop a list of prioritized infections for which new antimicrobial drug development is needed, among other duties. Within six years of the bill's enactment, the Government Accountability Office shall report to Congress a study on the bill's effectiveness in developing priority antimicrobial drugs.