The sequential and stochastic assignment problem (SSAP) has wide applications in logistics, finance, and health care management, and has been well studied in the literature. It assumes that jobs with unknown values arrive according to a stochastic process. Upon arrival, a job's value is made known and the decision-maker must immediately decide whether to accept or reject the job and, if accepted, to assign it to a resource for a reward. The objective is to maximize the expected reward from the available resources. The optimal assignment policy has a threshold structure and can be computed in polynomial time. In reality, there exist situations in which the decision-maker may postpone the accept/reject decision. In this research, we study the value of postponing decisions by allowing a decision-maker to hold a number of jobs which may be accepted or rejected later. While maintaining this queue of arrivals significantly complicates the analysis, optimal threshold policies exist under mild assumptions when the resources are homogeneous. We illustrate the benefits of delaying decisions through higher profits and lower risk in both cases of homogeneous and heterogeneous resources.