The present paper develops a simple theoretical setup to examine the role of the tax-spending mix of fiscal adjustments on aggregate (in)stability in indebted economies. To this end, we build an AK endogenous growth model with public debt dynamics. If the adjustment of the government's budget constraint is based on a single instrument (taxes or public spending), the economy converges towards a high-growth path. With mixed adjustment, however, another equilibrium appears (the no-growth path) that can be locally over-determine (unstable) or under-determined (stable). A hopf bifurcation can occurs at the border between the last two cases, which leads to cyclical dynamics. We also show that global indeterminacy is likely to emerge if fiscal adjustment is mainly based on public spending. A calibration of the model shows that area of indeterminacy covers reasonable values for parameters.