As it happens, the Supreme Court answered this question three decades ago in Heckler v. Chaney, which remains the leading case. In a decision joined by seven other justices, Justice William Rehnquist noted that, “This Court has recognized on several occasions over many years that an agency’s decision not to prosecute or enforce, whether through civil or criminal process, is a decision generally committed to an agency’s absolute discretion.”

There is, Rehnquist concluded, a “general presumption of unreviewability of decisions not to enforce”—unless the statute being administered “quite clearly withdrew discretion from the agency and provided guidelines for the exercise of its enforcement power.” The Heckler court, however, did endorse another standard that could trigger judicial review—namely, cases in which an agency has “consciously and expressly adopted a general policy that is so extreme as to amount to an abdication of its statutory responsibilities.”

Now comes the current controversy over how the Obama administration has chosen to implement the Immigration and Nationality Act. Here again there is a leading case—Arizona v. United States in 2012. Justice Anthony Kennedy observed for the majority that although Congress has specified which aliens may be removed from the U.S. and the procedures for doing so, “A principal feature of the removal system is the broad discretion exercised by immigration officials.”