Supreme Court Set to Hear Landmark Case: Key Ruling Looms on April 27th. A highly anticipated Supreme Court case is scheduled to be argued on April 27th, sparking intense debate and speculation among legal experts and observers. The case at the center of the controversy has been shrouded in secrecy, with details remaining scarce. However, sources indicate that the case involves a contentious issue that could have far-reaching implications for the nation. As the nation's highest court prepares to hear oral arguments, many are left wondering what the outcome will be and how it will impact the lives of Americans.