Inflation and the monetary financing of deficits are analyzed in a model in which the deficit is constrained to be less than a given fraction of a measure of aggregate market activity. Depending on parameter values, the model can have multiple steady states. Under adaptive learning with heterogeneous learning rules, there is convergence to a subset of these steady states. In some cases, a high-inflation constrained steady state will emerge. However, with a sufficiently tight fiscal constraint, the low-inflation steady state is globally stable. We provide experimental evidence in support of our theoretical results.