As several highly public scandals mount, Iraqi Prime Minister Muhammad Shia’ Al-Sudani is facing perhaps the most daunting threat to his political fortunes. Coming amid a dizzying array of economic, political, and social crises, allegations that his allies have been running an extensive wiretapping network have mobilized his opponents.

While notable in its own right, the wiretapping controversy has also served as a medium through which critics of the premier have focused opposition against Sudani’s rumored bid for a second term. It has also come to...