This paper addresses the question: how sensitive is the power of fiscal policy at the Zero Lower Bound (ZLB) to the assumption of rational expectations? We do so through the lens of a standard New Keynesian model in which people are dynamic level-k thinkers. Our analysis weakens the case for using government spending to stabilize the economy when the ZLB binds. The less sophisticated people are, the smaller the government-spending multiplier is. Our analysis strengthens the case for using tax policy to stabilize output when the ZLB is binding. The power of tax policy to stabilize the economy during the ZLB period is essentially undiminished when agents do not have rational expectations. Our results are robust to whether or not Ricardian equivalence holds. Finally, we show that the way in which tax policy is communicated is critical to its effectiveness.