This paper studies the dynamics of a New Keynesian dynamic stochastic general equilibrium (DSGE) model near the zero lower bound (ZLB) on nominal interest rates. In addition to the standard targeted-inflation equilibrium, we consider a deflation equilibrium as well as a Markov sunspot equilibrium that switches between a targeted-inflation and a deflation regime. We use the particle filter to estimate the state of the U.S. economy during and after the 2008-09 recession under the assumptions that the U.S. economy has been in either the targeted-inflation or the sunspot equilibrium. We consider a combination of fiscal policy (calibrated to the American Recovery and Reinvestment Act) and monetary policy (that tries to keep interest rates near zero) and compute government spending multipliers. Ex-ante multipliers (cumulative over one year) under the targeted-inflation regime are around 0.9. A monetary policy that keeps interest rates at zero can raise the multiplier to 1.7. The ex-post (conditioning on the realized shocks in 2009-11) multiplier is estimated to be 1.3. Conditional on the sunspot equilibrium, the multipliers are generally smaller and the scope for conventional expansionary monetary policy is severely limited.