We develop a taxonomical framework for classifying challenges to the possibility of consciousness in digital artificial intelligence systems. This framework allows us to identify the level of granularity at which a given challenge is intended (the levels we propose correspond to Marr's levels) and to disambiguate its degree of force: is it a challenge to computational functionalism that leaves the possibility of digital consciousness open (degree 1), a practical challenge to digital consciousness that suggests improbability without claiming impossibility (degree 2), or an argument claiming that digital consciousness is strictly impossible (degree 3)? We apply this framework to 14 prominent examples from the scientific and philosophical literature. Our aim is not to take a side in the debate, but to provide structure and a tool for disambiguating between challenges to computational functionalism and challenges to digital consciousness, as well as between different ways of parsing such challenges.