LOS ANGELES—Mayor Antonio Villaraigosa once organized for a teacher's union here, and later ran a branch of the American Federation of Government Employees. That makes him an unlikely advocate for cutting the benefits of the city's workers.

But with the city facing a budget deficit that could drain its reserves by summer, Mayor Villaraigosa wants to re-open contract talks with 45,000 cops, firefighters, librarians and other city employees in hopes of persuading them to contribute...