Final answer:
The "Mr. Madison's War" refers to the War of 1812, instigated by President James Madison in response to British maritime aggression and impressment of American sailors, which despite military challenges, is seen as an American victory symbolized by the Battle of New Orleans.
Step-by-step explanation:
The 19th-century war that was referred to derisively by the British public as "Mr. Madison's War" is the War of 1812. President James Madison, inheriting foreign relations problems from Thomas Jefferson and facing escalating hostility from British sea captains who impressed American sailors, was pushed by 'War Hawks' like Henry Clay and John C. Calhoun to declare war. Despite British naval superiority and American unpreparedness, illustrated by the army's size and the lack of a national bank, the U.S. managed to emerge from the conflict with a sense of victory, especially due to the Battle of New Orleans. The war ended with the Treaty of Ghent, which basically restored prewar boundaries but did not address the issue of impressment. The Federalist Party's opposition to the war, culminating in the Hartford Convention's talk of secession, eventually led to the party's demise.