In this paper, we consider multicast with Random Network Coding (RNC) over a wireless network using Orthogonal Frequency Division Multiple Access (OFDMA). Specifically, we propose a cross-layer resource allocation mechanism to minimize the total transmit power in the network to achieve a target throughput. The problem in its original form is a NP-hard mixed integer program. We alleviate this problem with a greedy power and subcarrier allocation algorithm that is combined with a node selection strategy that is enabled by RNC, which we refer to as "min-cut chasing". We compare it with a reference algorithm that assigns subcarriers independently based on the max-min fairness criterion followed by optimal power allocation. Our results reveal that the proposed greedy algorithm with min-cut chasing, which is of polynomial complexity, yields power savings of 3dB and is within 1dB of a lower bound based on an interference-free assumption.