Mass testing to identify and isolate infected individuals is a promising approach for reducing harm from the next acute respiratory virus pandemic. It offers the prospect of averting hospitalizations and deaths whilst avoiding the need for indiscriminate social distancing measures. To understand scenarios where mass testing might or might not be a viable intervention, here we modeled how effectiveness depends both on characteristics of the pathogen (R0, time to peak viral load) and on the testing strategy (limit of detection, testing frequency, test turnaround time, adherence). We base time-dependent test sensitivity and time-dependent infectiousness on an underlying viral load trajectory model. We show that given moderately high public adherence, frequent testing can prevent as many transmissions as more costly interventions such as school or business closures. With very high adherence and fast, frequent, and sensitive testing, we show that most respiratory virus pandemics could be controlled with mass testing alone.