Final answer:
The narrator means that Oliver was reluctant to take a breath as if he did not want to continue living.
Step-by-step explanation:
The phrase “there was considerable difficulty in inducing Oliver to take upon himself the office of respiration” means that Oliver was reluctant to take a breath as if he did not want to continue living. This statement is meant to convey how Oliver's condition was so dire that even the basic act of breathing seemed challenging. The narrator is describing the severity of Oliver's condition, indicating that he is in a critical state.