In environmental governance, local governments are the main actors, and their behavioral preferences between economic growth competition (EGC) and environmental regulation (ER) affect the inputs and outputs of environmental governance. Most studies discuss the relationship between government behaviors and the environment from the fiscal decentralization perspective, with few studies from the fiscal pressure (FP) perspective. Importantly, the bidirectional interaction mechanism is easily ignored. This study measured local government FP, EGC, ER, and environmental governance efficiency (EGE) in China's Yangtze River Delta (YRD) region from 2000 to 2020. Moran's I index was used to identify the change characteristics of local government behavioral preferences. The interaction mechanism was analyzed by a panel vector autoregression (PVAR) model. The results show that (1) from 2000 to 2020, FP was generally strengthened. EGE generally showed fluctuating and rising change characteristics, with more obvious fluctuating and rising characteristics before 2012 and after 2012, respectively. Local governments shifted from a strong alternative preference to a weak synergistic preference. (2) FP had a self-reinforcing effect. EGC and ER had a self-weakening effect. EGE had not only a self-weakening effect but also a weak self-dependence. (3) There is a double negative interaction mechanism between FP and local government behavioral preferences. FP made local governments prefer to reduce EGC and relax ER, but in fact, EGC and ER were conducive to alleviating FP. (4) There is a negative transitive influence mechanism between FP, local government behavioral preferences and EGE. The negative effect of FP on EGE can be transmitted by reducing EGC and ER. This paper provides a scientific basis for improving EGE in the YRD region and understanding the behavioral logic of local governments' environmental governance and a reference for other rapidly industrializing and urbanizing regions.