We introduce a mathematical model for studying the population dynamics under drought of the California newt (Taricha torosa), a species of special concern in the state of California. Since 2012, California has experienced a record-setting drought, and multiple studies predict drought conditions currently underway will persist and even increase in severity. Recent declines and local extinctions of California newt populations in Santa Monica Mountain streams motivate our study of the impact of drought on newt population sizes. Although newts are terrestrial salamanders, they migrate to streams each spring to breed and lay eggs. Since egg and larval stages occur in water, a precipitation deficit due to drought conditions reduces the space for newt egg-laying and the necessary habitat for larval development. To mathematically forecast newt population dynamics, we develop a nonlinear system of discrete equations that includes demographic parameters such as survival rates for newt life stages and egg production, which depend on habitat availability and rainfall. We estimate these demographic parameters using 15 years of stream survey data collected from Cold Creek in Los Angeles County, California, and our model captures the observed decline of the parameterized Cold Creek newt population. Based upon data analysis, we predict how the number of available newt egg-laying sites varies with annual precipitation. Our model allows us to make predictions about how the length and severity of drought can affect the likelihood of persistence and the time to critical endangerment of a local newt population. We predict that sustained severe drought will critically endanger the newt population but that the newt population can rebound if a drought is sufficiently short.