In non-cooperative bargaining games in the tradition of Rubinstein, the proposer derives bargaining power from the prospect of a costly delay which would follow the rejection of a proposal. We consider a unanimity bargaining game in which the proposer can strategically choose to prolong this delay. Prolonging the delay increases the proposer's bargaining power, but is assumed to come at a cost and thus cause an inefficiency. We use an appropriate refinement of stationary subgame-perfect equilibrium as the solution concept. We characterize equilibrium strategies and payoffs. We establish conditions on model parameters under which equilibrium is or is not efficient. For inefficient equilibria, we quantify the extent of the inefficiency. Moreover, we study the relation between the number of players and the degree of inefficiency. We find that inefficient equilibria become more inefficient the more players there are. Moreover, the parameter region in which an efficient equilibrium is possible shrinks when the number of players increases.