Fitting propensity (FP) analysis quantifies model complexity but has been impeded in item response theory (IRT) due to the computational infeasibility of uniformly and randomly sampling multinomial item response patterns under a full-information approach. We adopt a limited-information (LI) approach, wherein we generate data only up to the lower-order margins of the complete item response patterns. We present an algorithm that builds upon classical work on sampling contingency tables with fixed margins by implementing a Sequential Importance Sampling algorithm to Quickly and Uniformly Obtain Contingency tables (SISQUOC). Theoretical justification and omprehensive validation demonstrate the effectiveness of the SISQUOC algorithm for IRT and offer insights into sampling from the complete data space defined by the lower-order margins. We highlight the efficiency and simplicity of the LI approach for generating large and uniformly random data sets of dichotomous and polytomous items. We further present an iterative proportional fitting procedure to reconstruct joint multinomial probabilities after LI-based data generation, facilitating FP evaluation using traditional estimation strategies. We illustrate the proposed approach by examining the FP of the graded response model and generalized partial credit model, with results suggesting that their functional forms express similar degrees of configural complexity.