It is generally assumed that populations of a species will have similar responses to climate change, and thereby that a single value of sensitivity will reflect species-specific responses. However, this assumption is rarely systematically tested. High intraspecific variation will have consequences for identifying species- or population-level traits that can predict differences in sensitivity, which in turn can affect the reliability of projections of future climate change impacts. We investigate avian body condition responses to changes in six climatic variables and how consistent and generalisable these responses are both across and within species, using 21 years of data from 46 common passerines across 80 Dutch sites. We show that body condition decreases with warmer spring/early summer temperatures and increases with higher humidity, but other climate variables do not show consistent trends across species. In the future, body condition is projected to decrease by 2050, mainly driven by temperature effects. Strikingly, populations of the same species generally responded just as differently as populations of different species implying that a single species signal is not meaningful. Consequently, species-level traits did not explain interspecific differences in sensitivities, rather population-level traits were more important. The absence of a clear species signal in body condition responses implies that generalisation and identifying species for conservation prioritisation is problematic, which sharply contrasts conclusions of previous studies on the climate sensitivity of phenology.