In a seminal contribution, Schmitt-Grohé and Uribe (JPE, 1997), showed that the balanced-budget rule (BBR) produces aggregate instability in an exogenous growth model with labor tax-based adjustment. The present paper challenges this result in an endogenous growth framework with a more general budget rule, involving deficit and debt in the long-run and making the BBR a special case. We show that the emergence of aggregate instability dramatically depends on the level of public spending. In particular, low public spending ensures determinacy. However, in the case of high public spending, multiplicity arises, with four potential equilibria: two high-growth BGPs, a low-growth trap, and a "catastrophic" equilibrium where the economy asymptotically collapses. In addition, when the ratio of public spending is sufficiently large, a subcritical Hopf bifurcation appears around the low-growth trap, giving rise to a homoclinic orbit going around the neighborhood of the catastrophic equilibrium. A calibration exercise confirms that these results are obtained for realistic values of parameters.