Final answer:
The famous New York City Democratic political machine was known as Tammany Hall, which under 'Boss' Tweed's leadership, controlled the city's politics through graft and bribery in exchange for votes and political support.
Step-by-step explanation:
The famous New York City Democratic political machine was known as Tammany Hall. Led by William “Boss” Tweed, Tammany Hall was the epitome of a political machine during the 19th century, exercising control from the 1850s to the 1930s. Citizens would often turn to the machine for immediate solutions to their problems, like the building of sidewalks in little Italy, bypassing city hall bureaucracy. In return, political support and votes were expected in future elections. However, this system was notorious for its corrupt practices, including graft and bribery. Machines like Tammany Hall offered timely aid and handled urban issues but at the cost of ethical governance.