We propose a new model of legislative bargaining in which coalitions may have different values, reflecting the fact that the policies they can pursue are constrained by the identity of the coalition members. As the delay between offers goes to zero, the equilibrium allocation of the model converges to a generalized version of a Nash bargaining solution in which-in contrast to the standard solution-the winning coalition is endogenous and determined by the relative coalitional values. A form of the holdup problem specific to these bargaining games contributes to generate significant inefficiencies in the selection of the coalition. The model helps rationalize well-known empirical facts that are in conflict with the predictions of standard noncooperative models of bargaining.