Deep learning-based drug response prediction (DRP) methods can accelerate the drug discovery process and reduce research and development costs. Despite their high accuracy, generating regression-aware representations remains challenging for mainstream approaches. For instance, the representations are often disordered, aggregated, and overlapping, and they fail to characterize distinct samples effectively. This results in poor representation during the DRP task, diminishing generalizability and potentially leading to substantial costs during the drug discovery. In this paper, we propose CLDR, a contrastive learning framework with natural language supervision for the DRP. The CLDR converts regression labels into text, which is merged with the drug response caption as a second sample modality instead of the traditional modes, i.e., graphs and sequences. Simultaneously, a common-sense numerical knowledge graph is introduced to improve the continuous text representation. Our framework is validated using the genomics of drug sensitivity in cancer dataset with average performance increases ranging from 7.8% to 31.4%. Furthermore, experiments demonstrate that the proposed CLDR effectively maps samples with distinct label values into a high-dimensional space. In this space, the sample representations are scattered, significantly alleviating feature overlap. The code is available at: https://github.com/DrugD/CLDR.