This study investigates how the government fiscal stimulus policy affects public-debt sustainability and the unemployment rate. We analyze an economy with an imperfect labor market in which the government maintains its budget from tax revenue and public debt. We assume that the government's income transfer is fiscal stimulus policy and show that the policy reduces the unemployment rate, increases the economy's growth rate, and raises the threshold of the ratio of public debt to private capital that is needed to sustain public debt. The arguments presented show that an income transfer policy may generate an economy that not only is sustainable with regard to public debt but also has a low unemployment rate in the long run.