The coalition includes the Service Employees International Union, the Labor Council for Latin American Advancement, the League of United Latin American Citizens, the National Association of Latino Elected and Appointed Officials, Mi Familia Vota, Voto Latino and the Hispanic Federation.
Their demands for immigration legislation include a comprehensive package and what they call a "path to citizenship."
While conservative leaders have said the Republican Party needs to be more welcoming to the nation's fastest-growing voting bloc, granting a path to citizenship - which some liken to amnesty - will be difficult for many to embrace.
Republican supporters of immigration legislation, such as Sen. Marco Rubio of Florida, have indicated a preference for a package of laws that address border security, guest-worker programs and undocumented students as individual issues, rather than pushing one massive piece of legislation that would be more difficult to pass.
But Ben Monterroso, the national executive director of Mi Familia Vota, said both parties no longer could use the Latino community as a political football. And Murguia warned Obama that failure to pass comprehensive immigration legislation would leave him with a legacy as the president who deported more people than any other.
Coalition participants plan to rank members of Congress based on their support of immigration legislation. Eliseo Medina, the secretary-treasurer of the Service Employees International Union, warned that those who "work against us or simply sit by idly" will pay a price in 2014.
"We welcome everyone into this battle," Medina said. "Republicans and Democrats. By God, maybe they can get a 'Kumbaya' moment."