Aviation technologies and concepts have reached a level of maturity that may soon enable an era of on-demand mobility (ODM) fueled by quiet, efficient, and largely automated air taxis. However, successfully bringing such a system to fruition will require introducing orders-of-magnitude more aircraft to a given airspace volume than can be accommodated by the traditional air traffic control system, among other important technical challenges. The airspace integration problem is further compounded by requirements to set aside appropriate ground infrastructure for take-off and landing areas and ensuring these new aircraft types and their operations do not overly burden traditional airspace users and air traffic control. These challenges for ODM may be significantly reduced by extending the concepts and technologies developed to manage small unmanned aircraft systems (UAS) at low altitude "the UAS traffic management (UTM) system" to higher altitudes and aircraft with humans onboard in controlled airspace, or by equipping ODM aircraft with advanced sensors, algorithms, and interfaces. The precedent of operational freedom inherent in visual flight rules and the technologies developed for large UAS and commercial aircraft automation will contribute to the evolution of an ODM system enabled by UTM. This paper describes the set of air traffic services, normally provided by the traditional air traffic system, that an ODM system would implement to achieve the high densities needed for ODM's economic viability. Finally, the paper proposes a framework for integrating, evaluating, and deploying low-, medium-, and high-density ODM concepts that build on each other to ensure operational and economic feasibility at every step.