“You look around at who has the most difficult jobs, at who is doing the work we rely on every day, and it is immigrants,” Ms. Durazo said in an interview here. “If we look at what we can do for them, what we can do together, we see that there can be very important rewards that will improve their lives. We cannot fix the prosperity of the rest of the country without improving the prosperity of immigrants.”

It is impossible to know just how many of the roughly 800,000 union members in Los Angeles are in the country illegally, often using fake Social Security numbers or other forged papers. But the county has an estimated 900,000 illegal immigrants, more than any other in the country, and according to the Center for the Study of Immigrant Integration at the University of Southern California they make up about 9 percent of the state’s work force.

The power of the heavily immigrant unions can be seen in huge protests in Los Angeles, as well as in the extensive voter outreach operations across the city. And while Ms. Durazo remains focused on the immigration debate in Congress, she is simultaneously marshaling her troops to help elect a new mayor here and prevent the sale of The Los Angeles Times to the conservative billionaires Charles G. Koch and David H. Koch.

In the mayoral race, the unions have backed Wendy Greuel, the city controller, against Eric M. Garcetti, a city councilman, and have spent millions helping her. This week, the union mailed fliers suggesting that if Ms. Greuel was elected, the minimum wage would be raised to $15. Ms. Greuel has said she would support raising wages at the city’s largest hotels to $15, but has not backed a citywide increase.

Ms. Durazo has often enraged local business leaders, but successful campaigns to require a living wage in some of the city’s hotels and to unionize carwash workers have earned her respect and devotion among many immigrants, who often line up to see her as she travels around the country.