This article analyzes the combined parameter and state identifiability for a model of a cancerous tumor's growth dynamics. The model describes the impact of drug administration on the growth of two populations of cancer cells: a drug-sensitive population and a drug-resistant population. The model's dynamic behavior depends on the underlying values of its state variables and parameters, including the initial sizes and growth rates of the drug-sensitive and drug-resistant populations, respectively. The article's primary goal is to use Fisher identifiability analysis to derive and analyze the Cramér–Rao theoretical bounds on the best-achievable accuracy with which this estimation can be performed locally. This extends previous work by the authors, which focused solely on state estimation accuracy. This analysis highlights two key scenarios where estimation accuracy is particularly poor. First, a critical drug administration rate exists where the model's state observability is lost, thereby making the independent estimation of the drug-sensitive and drug-resistant population sizes impossible. Second, a different critical drug administration rate exists that brings the overall growth rate of the drug-sensitive population to zero, thereby worsening model parameter identifiability.