Phenotypic plasticity is an important mechanism for populations to respond to fluctuating environments, yet may be insufficient to adapt to a directionally changing environment. To study whether plasticity can evolve under current climate change, we quantified selection and genetic variation in both the elevation (RNE) and slope (RNS) of the breeding time reaction norm in a long‐term (1973–2016) study population of great tits (Parus major). The optimal RNE (the caterpillar biomass peak date regressed against the temperature used as cue by great tits) changed over time, whereas the optimal RNS did not. Concordantly, we found strong directional selection on RNE, but not RNS, of egg‐laying date in the second third of the study period; this selection subsequently waned, potentially due to increased between‐year variability in optimal laying dates. We found individual and additive genetic variation in RNE but, contrary to previous studies on our population, not in RNS. The predicted and observed evolutionary change in RNE were, however, marginal, due to low heritability and the sex limitation of laying date. We conclude that adaptation to climate change can only occur via micro‐evolution of RNE, but this will necessarily be slow and potentially hampered by increased variability in phenotypic optima.