The wide range of cost estimates for stabilizing climate is puzzling to policy makers as well as researchers. Assumptions about technology costs have been studied extensively as one reason for these differences. Here, we focus on how policy timing and the modeling of economy-wide interactions affect costs. We examine these issues by restructuring a general equilibrium model of the global economy, removing elements of the model one by one. We find that delaying the start of a global policy by 20 years triples the needed starting carbon price and increases the macroeconomic cost by nearly 30%. We further find that including realistic details of the economy (e.g. sectoral and electricity technology detail; tax and trade distortions; capital vintaging) more than double net present discounted costs over the century. Inter-model comparisons of stabilization costs find a similar range, but it is not possible to isolate the structural causes behind cost differences. Broader comparisons of stabilization costs face the additional issue that studies of different vintages assume different policy starting dates, often dates that are no longer realistic given the pace of climate change negotiations. This study can aid in interpretation of estimates and give policymakers and researchers an idea of how to adjust costs upwards as the start of policy is delayed. It also illustrates that models that greatly simplify the realities of modern economies likely underestimate costs.