This paper proposes the integration and analysis of a mathematical model representing the cardiovascular system and its short-term autonomic response to head-up tilt (HUT) testing. A Latin Hypercube Sampling method was applied to design an optimal experimental space, including 19 model parameters coming from the cardiovascular and baroreflex control systems. Then, a global, variance-based sensitivity analysis was applied to quantity the effects of these parameters on heart rate and systolic blood pressure. Results highlight the relevant influence of the intrinsic heart rate and the sympathetic and parasympathetic baroreflex gains on heart rate regulation, as well as the impact of left ventricle diastolic parameters on systolic blood pressure. Moreover, a significant effect of right ventricle dynamics on blood pressure was noted. These results provide valuable information for the application of such an integrated model for the analysis of the autonomic mechanisms regulating the cardiovascular response induced by postural changes. In particular, they suggest a convenient set of parameters to be identified in a subject-specific manner.