Bad news for those huddled masses yearning to breathe free: The federal government is offering $1 billion to hospitals that provide emergency care to undocumented immigrants. But to get the money, hospitals would have to ask patients about their immigration status, a prospect that alarms hospitals and advocates for immigrants....Hospital executives and immigrant rights groups said the questioning would deter undocumented immigrants from seeking hospital care when they need it, and some hospitals said compliance might cost them more than they would receive in federal aid. Marcela G. Urrutia, an analyst at the National Council of La Raza, a Hispanic civil rights group, said: "We are extremely concerned about this requirement. It will deter Latino communities from seeking emergency care. That could lead to serious public health problems, including the spread of communicable diseases.'' Janelle R. Howard, a spokeswoman for Carondelet Health Network, with hospitals in Tucson and Nogales, Ariz., said: "Our emergency rooms see a lot of undocumented immigrants, including some picked up in the desert. But as a Catholic institution, we have never asked about their immigration status. It's our mission and philosophy to treat all without distinction.''