Recent studies of cosmology in the presence of a small fundamental cosmological constant (hep-th/0208013) concluded that in that picture inflation is not the likely path to the state of the current observed universe. In fact, neither is the standard big bang. In this talk I scrutinize the failure modes of the standard cosmology in that picture, and consider 1) Whether these problems are robust in the case of a small cosmological constant and 2) Whether similar problems might persist in other frameworks. I also identify the key assumptions about causal patch physics that cause the problems in the first place.