Cocaine addiction is a significant and complex disease. Part of this complexity is caused by the variability of the drug experience early in drug use (initial responsiveness, amount of use, etc.). In rats, individual differences in initial cocaine responsiveness and cocaine self-administration history both predict the development of cocaine sensitization, a putative mechanism contributing to the development of cocaine addiction. Here, we sought to determine the role of these factors and cocaine dose on the development of sensitization to cocaine's motivational effects during the earliest stages of self-administration. Rats were classified as either low or high cocaine responders (LCRs or HCRs, respectively) based on acute cocaine-induced locomotor activity (10 mg/kg i.p.) before learning to self-administer cocaine (0.6 mg/kg/infusion i.v.) under a fixed ratio 1 (FR1) schedule of reinforcement. After acquisition, rats self-administered cocaine (0.6 or 1.2 mg/kg/infusion) under a progressive ratio (PR) schedule of reinforcement either immediately or after an additional five FR1 sessions (0.6 or 1.2 mg/kg/infusion). No LCR/HCR differences in sensitization were observed. However, regardless of LCR/HCR classification, exposure to the higher dose of cocaine produced sensitization to cocaine's motivational effects on the PR schedule (i.e., increased break points) and an escalation of consumption on the FR schedule. Thus, our results reveal a novel model for studying escalation and sensitization very early after acquisition and suggest that sensitization may be important in the earliest stages of the cocaine addiction process.