There is a great need for antiviral drugs to treat enterovirus (EV) and rhinovirus (RV) infections, which can be severe and occasionally life-threatening. The conserved nonstructural protein 2C, which is an AAA+ ATPase, is a promising target for drug development. Here, we present a structure-activity relationship study of a previously identified compound that targets the 2C protein of EV-A71 and several EV-B species members, but not poliovirus (PV) (EV-C species). This compound is structurally related to the Food and Drug Administration (FDA)-approved drug fluoxetine—which also targets 2C—but has favorable chemical properties. We identified several compounds with increased antiviral potency and broadened activity. Four compounds showed broad-spectrum EV and RV activity and inhibited contemporary strains of emerging EVs of public health concern, including EV-A71, coxsackievirus (CV)-A24v, and EV-D68. Importantly, unlike (S)-fluoxetine, these compounds are no longer neuroactive. By raising resistant EV-A71, CV-B3, and EV-D68 variants against one of these inhibitors, we identified novel 2C resistance mutations. Reverse engineering of these mutations revealed a conserved mechanism of resistance development. Resistant viruses first acquired a mutation in, or adjacent to, the α2 helix of 2C. This mutation disrupted compound binding and provided drug resistance, but this was at the cost of viral fitness. Additional mutations at distantly localized 2C residues were then acquired to increase resistance and/or to compensate for the loss of fitness. Using computational methods to identify solvent accessible tunnels near the α2 helix in the EV-A71 and PV 2C crystal structures, a conserved binding pocket of the inhibitors is proposed.