We consider the performance of information propagation through social networks in a scenario where each user has a budget of attention, that is, a constraint on the frequency with which he pulls content from neighbors. In this context we ask the question "when users make selfish decisions on how to allocate their limited access frequency among neighbors, does information propagate efficiently?" For the metric of average propagation delay, we provide characterizations of the optimal social cost and the social cost under selfish user optimizations for various topologies of interest. Three situations may arise: well-connected topologies where delay is small even under selfish optimization; tree-like topologies where selfish optimization performs poorly while optimal social cost is low; and "stretched" topologies where even optimal social cost is high. We propose a mechanism for incentivizing users to modify their selfish behaviour, and observe its efficiency in the family of tree-like topologies mentioned above.