ALEXANDRIA—It looks as if the growing scandal involving Gov. Bob McDonnell’s family and a wealthy donor are starting to hurt the governor’s approval ratings.

The breadth of the approval plunge is surprising even pollsters.

McDonnell’s net approval rating took a 12-point dive over the past month, putting him in negative numbers for the first time since he took office, according to a poll released Monday from Public Policy Polling. Only 36 percent of those polled approved of McDonnell’s performance as governor; 41 percent disapproved.