We propose a novel framework where forward guidance (FG) is endogenously determined. Our model assumes that a monetary authority solves an optimal policy problem under commitment at the zero-lower bound. FG derives from two sources: 1. from commiting to keep interest rates low at the exit of the liquidity trap, to stabilize inflation today. 2. From debt sustainability concerns, when the planner takes into account the consolidated budget constraint in optimization. Our model is tractable and admits an analytical solution for interest rates in which 1 and 2 show up as separate arguments that enter additively to the standard Taylor rule. In the case where optimal policy reflects debt sustainability concerns (satisfies the consolidated budget) monetary policy becomes subservient to fiscal policy, giving rise to more volatile inflation, output and interest rates. Liquidity trap (LT) episodes are longer, however, the impact of interest rate policy commitments on inflation and output are moderate. "Keeping interest rates low" for a long period, does not result in positive inflation rates during the LT, in contrast our model consistently predicts negative inflation at the onset of a LT episode. In contrast, in the absence of debt concerns, LT episodes are shorter, but the impact of commitments to keep interest rates low at the exit from the LT, on inflation and output is substantial. In this case monetary policy accomplishes to turn inflation positive at the onset of the episode, through promising higher inflation rates in future periods. We embed our theory into a DSGE model and estimate it with US data. Our findings suggest that FG during the Great Recession may have partly reflected debt sustainability concerns, but more likely policy reflected a strong commitment to stabilize inflation and the output gap. Our quantitative findings are thus broadly consistent with the view that the evolution of debt aggregates may have had an impact on monetary policy in the Great Recession, but this impact is likely to be small.