About a quarter of Illinois’ 102 counties will stop paying local prosecutors and public defenders within one or two months, a state’s attorneys group has said.LaSalle County State’s Attorney Brian J. Towne, chairman of the appellate prosecutor office, told a House committee this week that funds for many local public lawyers will dry up in 30 to 60 days if the state budget impasse continues.And that could lead to slow-downs in court cases and speedy-trial issues in those counties.“Without the funds …