The impulsive ankle push-off is crucial for natural leg dynamics and efficiency in human walking. To study the biomechanics of the ankle push-off, we use 2D predictive neuromuscular simulations. Assessing the sensitivity of model outputs to input variations is necessary to evaluate the reliability of model predictions. Sensitivity analysis (SA) can quantify how uncertainty in model outputs is related to different sources of uncertainty in model inputs. This work presents a new open-source software framework for global SA of predictive neuromuscular simulations using SCONE-Hyfydy and the SAFE toolbox. With the framework, we investigate how sensitive the ankle push-off and related gait characteristics are to variations in muscle-tendon unit (MTU) stiffness and tendon slack length (TSL) of Soleus (SOL), Gastrocnemius (GAS), and hip flexor muscles (HFL), the muscles active during push-off. To characterize the quality of the ankle push-off, we evaluate the models' maximum positive ankle power, maximum normalized cross-correlation of simulated ankle kinematics with human data to assess the signal similarity, cost of transport (CoT), and walking speed. Four different SA methods are compared: EET, FAST, PAWN, and VBSA. We found GAS MTU stiffness and TSL to have a significant impact on the models' CoT, walking speed, and ankle kinematics. Variations of SOL and HFL properties had limited to no effect on the assessed outputs. The four SA methods showed similar trends, but the computational costs and detailed results varied. With this work, we provide the biomechanics community with a software framework for SA of predictive neuromuscular simulations. Our results will improve the functional understanding of the ankle push-off, aiding in developing robotic devices and prostheses.