Disasters lead to devastating structural damage not only to buildings and transport infrastructure, but also to other critical infrastructure, such as the power grid and communication backbones. Following such an event, the availability of minimal communication services is however crucial to allow efficient and coordinated disaster response, to enable timely public information, or to provide individuals in need with a default mechanism to post emergency messages. The Internet of Things consists in the massive deployment of heterogeneous devices, most of which battery-powered, and interconnected via wireless network interfaces. Typical IoT communication architectures enables such IoT devices to not only connect to the communication backbone (i.e. the Internet) using an infrastructure-based wireless network paradigm, but also to communicate with one another autonomously, without the help of any infrastructure, using a spontaneous wireless network paradigm. In this paper, we argue that the vast deployment of IoT-enabled devices could bring benefits in terms of data network resilience in face of disaster. Leveraging their spontaneous wireless networking capabilities, IoT devices could enable minimal communication services (e.g. emergency micro-message delivery) while the conventional communication infrastructure is out of service. We identify the main challenges that must be addressed in order to realize this potential in practice. These challenges concern various technical aspects, including physical connectivity requirements, network protocol stack enhancements, data traffic prioritization schemes, as well as social and political aspects.