While LTE is becoming widely rolled out for human-type services, it is also a promising solution for cost-efficient connectivity of the smart grid monitoring equipment. This is a type of machine-to-machine (M2M) traffic that consists mainly of sporadic uplink transmissions. In such a setting, the amount of traffic that can be served in a cell is not constrained by the data capacity, but rather by the signaling constraints in the PRACH, PDCCH, and PUSCH channels. In this paper we explore these limitations using a detailed simulation of the LTE access reservation protocol (ARP). We find that 1) assigning RAOs more frequently sometimes worsens performance; and 2) the additional signaling that follows the ARP has very large impact on the capacity in terms of the number of supported devices; we observed a reduction in the capacity by almost a factor of 3. This suggests that a lightweight access method, with reduced number of signaling messages, needs to be considered in standardization for M2M applications. Additionally we propose a tractable analytical model that accurately evaluates the outage for a given scenario at click-speed. The model accounts for the features of the PRACH, PDCCH, PDSCH, and PUSCH, as well as retransmissions.