We study the conformational properties of polymers in room temperature ionic liquids using theory and simulations of a coarse-grained model. Atomistic simulations have shown that single poly(ethylene oxide) (PEO) molecules in the ionic liquid 1-Butyl 3-Methyl Imidazolium tetrafluoroborate ([BMIM][BF4]) are expanded at room temperature, i.e., the radius of gyration, R-g, scales with molecular weight, M-w, as R-g similar to M-w(0.9), instead of the expected self-avoiding walk behavior. The simulations were restricted to fairly short chains, however, which might not be in the true scaling regime. In this work we investigate a coarse-grained model for the behavior of PEO in [BMIM][BF4]. We use existing force fields for PEO and [BMIM][BF4] and Lorentz-Berthelot mixing rules for the cross interactions. The coarse-grained model predicts that PEO collapses in the ionic liquid. We also present an integral equation theory for the structure of the ionic liquid and the conformation properties of the polymer. The theory is in excellent agreement with the simulation results. We conclude that the properties of polymers in ionic liquids are unusually sensitive to the details of the intermolecular interactions. The integral equation theory is sufficiently accurate to be a useful guide to computational work.