It is important to identify scalability constraints in existing job scheduling software as they are applied to next generation parallel systems. In this paper, we analyze the scalability of job scheduling and job dispatching functions in the IBM LoadLeveler job scheduler. To enable this scalability study, we propose and implement a new virtualization method to deploy different size LoadLeveler clusters with minimal number of physical machines. Our scalability studies with the virtualization show that the LoadLeveler resource manager can comfortably handle over 12,000 compute nodes, the largest scale we have tested so far. However, our study shows that the static resource matching in the scheduling cycle and job object processing during the hierarchical job launching are two impediments for the scalability of LoadLeveler.