Social Security's Office of Inspector General (OIG) has produced a report about the agency's employees who are delinquent in paying their federal taxes. See below for a chart. I'd call it sort of a gotcha report, good for little more than helping those who want to criticize civil servants.
Social Security employees are in about the same range as other federal employees when it comes to tax delinquency.
By the way, the report shows that 1.8% of Social Security's Administrative Law Judges and 1.2% of its Senior Executive Service employees are tax delinquent.
I didn't see any comparable numbers for non-federal government workers. I'd bet it's considerably higher.