The paper focuses on supply side funding gaps inherent to financial inclusion schemes that threaten their efficacy and sustainability. We model the double bind problem that providers of banking services for the poor face as they struggle to achieve economies of scale to drive down average fixed financial infrastructure costs, while average account balances are low due to insufficient income. This model is applied to the Prime Minister Jan-Dhan Yojna (PMJDY) financial inclusion scheme in India, that was started in 2014. An innovative approach based on cross sectional bank level data from 2014 till 2017 is used to quantify the incentives and costs involved in targeting unbanked households. This gives a monetary estimate of the economic shortfalls or surpluses for participating banks, measured as bank balances relative to outlay costs and subsidies per PMJDY beneficiary. A lack of economic viability of PMJDY accounts is found in the majority of Indian public sector banks, a matter which is problematic in view of their extant financial fragility. We provide evidence for cross subsidization of rural bank accounts by urban accounts. We use fixed effects panel methods to determine what cost public sector banks bear and also quantify the extent to which account ineffectiveness is ameliorated by exogenous factors, primarily the tie up of PMJDY accounts with bio-metric Aadhar cards and electronic direct benefit transfer of G2P payments.