Well the executive branch (which the President heads) is responsible for "[executing and enforcing] orders of the court through federal law enforcement" (wikipe

Well the executive branch (which the President heads) is responsible for "[executing and enforcing] orders of the court through federal law enforcement" (wikipedia). So, the courts decide how the law is applied, but the executive branch enacts the orders as given by the judicial branch, and is thus also responsible for determining when exceptions are to be made to the enactment of those orders.