In large-value real-time gross settlement payment systems, banks rely heavily on incoming funds to finance outgoing payments. Such reliance necessitates a high degree of coordination and synchronization. We construct a model of a payment system calibrated for the U.S. Fedwire system and examine the impact of realistic disruptions motivated by the recent financial crisis. In such settings, individually cautious behavior can have a significant and detrimental impact on the overall functioning of the payment system through a multiplier effect. Our results quantify the mutually reinforcing nature of greater caution, and allow comparative statics analysis of shifts in key parameters.