Shortest Remaining Processing time (SRPT) has long been known to optimize the queue length distribution and the mean response time (a.k.a. flow time, sojourn time). As such, it has been the focus of a wide body of analysis. However, results about the heavy-traffic behavior of SRPT have only recently started to emerge. In this work, we characterize the growth rate of the mean response time under SRPT in the M/GI/1 system under general job size distributions. Our results illustrate the relationship between the job size tail and the heavy traffic growth rate of mean response time. Further, we show that the heavy traffic growth rate can be used to provide an accurate approximation for mean response time outside of heavy traffic regime.