Government agencies typically need to take potential risks of disclosure into account whenever they publish statistics based on their data or give external researchers access to collected data. In this context, the promise of formal privacy guarantees offered by concepts such as differential privacy seems to be the panacea enabling the agencies to quantify and control the privacy loss incurred by any data release exactly. Nevertheless, despite the excitement in academia and industry, most agencies -- with the prominent exception of the U.S. Census Bureau -- have been reluctant to even consider the concept for their data release strategy. This paper discusses potential reasons for this. We argue that the requirements for implementing differential privacy approaches at government agencies are often fundamentally different from the requirements in industry. This raises many challenges and questions that still need to be addressed before the concept can be used as an overarching principle when sharing data with the public. The paper does not offer any solutions to these challenges. Instead, we hope to stimulate some collaborative research efforts, as we believe that many of the problems can only be addressed by interdisciplinary collaborations.