Final answer:
The Marbury v. Madison case established the principle of judicial review, granting the U.S. Supreme Court the power to declare acts of Congress unconstitutional and securing its role as a significant fixture in the governmental process.
Step-by-step explanation:
The ruling in Marbury v. Madison had a profound effect on the U.S. Supreme Court by establishing the principle of judicial review. This principle gave the Court the authority to nullify Congressional acts that it found to be unconstitutional, effectively checking the powers of the legislative and executive branches. The case was brought to the Supreme Court when William Marbury petitioned for his commission as justice of the peace in the District of Columbia, which had not been delivered by Jefferson's Secretary of State, James Madison. Chief Justice John Marshall, mindful of the political tensions between Federalists and Republicans, crafted a ruling that resolved the case while also asserting the right of the Court to declare an act of Congress unconstitutional. As a result, the Supreme Court was established as the final arbiter of constitutional interpretation, a central fixture in the balance of powers within the U.S. government.
The decision simultaneously affirmed Marbury's legal rights, avoided direct conflict with President Jefferson, and cleverly declined the Court's short-term power in favor of establishing its long-term role in guiding national policy. It reinforced the independence and influence of the judicial branch and has since played a critical role in ensuring the Constitution remains the supreme law of the land.