Under extreme disturbances, the safety of natural gas pipeline networks is governed by transient capabilities to sustain fuel delivery rather than steady-state balance. Existing studies, often grounded in static assumptions, fail to capture the nonlinear coupling among linepack dynamics, operational regulation, and demand response. To address this limitation, this study proposes a resilience-oriented optimization approach that integrates transient hydraulics with priority-based load shedding. From an operational perspective, system response to extreme disturbances can be interpreted through a hierarchical defense mechanism comprising passive buffering, active regulation, and adaptive degradation. Two metrics, system survival time and resilience limit, are introduced to quantify the operational boundaries of emergency conditions. A nonlinear programming model is developed by explicitly coupling transient flow equations, compressor constraints, and time-dependent response delays. Case studies on supply interruption and demand surge scenarios reveal distinct mechanisms governing system resilience. In supply interruption scenarios, resilience relies on the synergy between linepack buffering and intervention timing; notably, decision latency is found to nonlinearly amplify the required load shedding intensity. Explicitly utilizing this temporal buffer can reduce required load shedding by approximately 74% compared to steady-state models. Conversely, under demand surge scenarios, system failure is dictated by topological transmission bottlenecks (identified at a 32% demand surge limit), indicating that operational regulation alone cannot break through the inherent resilience ceiling. Furthermore, effective load shedding strategies must account for the spatial hydraulic effectiveness of demand nodes. These findings provide a physically grounded quantification of emergency operability, offering quantitative operational insights for emergency scheduling and resilience-oriented decision-making in natural gas pipeline systems.