We consider a single-hop data gathering sensor cluster consisting of a set of sensor nodes that need to transmit data periodically to a base-station. We are interested in maximizing the lifetime of this network. Even though the setting of our problem is very simple, it turns out that the solution is far from easy. The complexity arises from several competing system-level opportunities to be harnessed to reduce the energy consumed in radio transmission. First, sensor data in a cluster is spatially and temporally correlated. Recent advances in distributed source coding allow us to take advantage of these correlations to reduce the number of bits that need to be transmitted, with concomitant savings in energy. Second, it is also well known that channel coding can be used to reduce transmission energy by increasing transmission time. Finally, sensor nodes are cooperative, unlike nodes in an ad hoc network that are often modeled as competitive. This collaborative nature allows us to take full advantage of the first two opportunities for the purpose of maximizing cluster lifetime. In this paper, we pose the problem of maximizing lifetime as a max-min optimization problem subject to the constraint of successful data collection and limited energy supply at each node. This turns out to be an extremely difficult optimization to solve. Consequently, we employ a notion of instantaneous decoding to shrink the problem space. We show that the computational complexity of our model is determined by the relationship between energy consumption and transmission rate as well as model assumptions about path loss and initial energy reserves. We provide some algorithms, heuristics and insight for several scenarios. In some situations our problem admits a greedy solution while in other the problem is shown to be NP-hard. The chief contribution of the paper is to illustrate both the challenges and gains provided by source-channel coding and scheduling.