Political corruption---the misuse of political office for personal or political gain---is corrosive for economic growth, political stability, and citizen satisfaction. Yet, considerable efforts in promoting strong anti-corruption institutions and policies have had at best limited success in many developing democracies. "Supply side" factors such as low state capacity or lack of political will are often blamed for such lack of progress. By contrast, we examine the constraints on good governance reforms posed by the "demand side"---the public itself. We argue that citizens' dissatisfaction with widespread corruption in many countries can make them more supportive of and receptive to anti-corruption `by any means necessary,' including potentially illiberal and illegal methods such as blanket wiretaps or no-bail pretrial detention. Coupled with strong partisan preferences present in many competitive democracies, this tolerance for illiberal anti-corruption methods may create illiberal anti-corruption double standards, whereby citizens condone the use of harsh measures against partisan opponents, while opposing such measures---or any anti-corruption measures---when directed at co-partisans. This preference structure can delegitimize good governance reforms and leave them vulnerable to politicization by strategic (and potentially corrupt) elites. Using data from survey and natural experiments in Romania---a country with marked corruption, engaged populace and activist anti-corruption policies---we find evidence consistent with our expectations.