The 1803 case of Marbury vs. Madison set a precedent for how the Supreme Court sees and decides cases still today. How does Marbury vs. Madison affect the Supreme Court presently? The Supreme Court has judicial review allowing it to deem things unconstitutional. The Supreme Court was weakened by the case and remains weak today. The Supreme Court is able to compel Congress to act in a certain way. Congress of the Executive Branch can overrule the Supreme Court