Is aggressive monetary policy response to inflation feasible in countries that suffer from fiscal dominance? We find that if nominal interest rates are allowed to respond to government debt, even aggressive rules that satisfy the Taylor principle can produce unique equilibria. However, resulting inflation is extremely volatile and zero lower bound on nominal interest rates is frequently violated. Within the set of feasible rules the optimal response to inflation is highly negative, and more aggressive inflation fighting is inferior from a welfare point of view. The welfare gain from responding to fiscal variables is minimal compared to the gain from eliminating fiscal dominance.