Following Portugal's bailout, several measures concerning the rationalization of resources of the national health system have been recommended, aiming to improve the efficiency of services and generate additional savings. Our purpose is to approach this issue by asking for its conformity with the Constitution of the Portuguese Republic, and by further characterizing and discussing the right to health as a typical social right, the implementation of which presupposes the "reserve of what is possible" (including its dependence on existing economic resources). By taking into account a critical overview of the legal / constitutional doctrine, our analysis will focus on the relevant constitutional precept (art. 64, d), No. 3,) - which remits to the principle of economy in the provision of public services - and on the methodological challenges concerning the sustainability of the welfare state. We arrive at the doctrine of the "essential core" of social rights, followed by the discussion of how to determine the "essential core" of the right to health. As an example, we will discuss the sensitive issue of drugs prescription, clinical guidelines and governance, and forms by which prescribing patterns may be built. According to our approach, the essential core of the right to health for all (protected by the Constitution) presupposes the improvement of efficiency and the principle of economy in the National Health System.