Immigrants supported political machines because the machines provided jobs, services and support that the government did not. This was particularly important in the late 19th century, when urban populations began to boom.
The massive increase in urban populations was due in large part to immigration. This influx of immigrants packed cities with people, but the cities lagged behind in offering sewers, living quarters, welfare and other benefits to ease life in a new country for the new citizens, who were often poorly educated and unable to speak English. The machines saw this as an opportunity.
Often, representatives of a political machine would meet new immigrants as they came in to the country. He or she would provide the immigrants with a place to live and perhaps even a job. In exchange, the immigrants were expected to vote for a political machines' candidates for public office. Because immigrants typically had little prior ideological affiliation, such a pragmatic exchange made sense. This practice allowed political machines like Tammany Hall to dominate politics in urban centers like New York City for several decades. Although such machines were dens of corruption, and the patronage jobs they offered to supporters often undermined efficiency, they did allow new Americans to have a step up in their adopted country.