Integrated assessment models are commonly used to generate optimal carbon prices based on an objective function that maximizes social welfare. Such models typically project an initially low carbon price that increases with time. This framework does not reflect the incentives of decision makers who are responsible for generating tax revenue. If a rising carbon price is to result in near-zero emissions, it must ultimately result in near-zero carbon tax revenue. That means that at some point, policy makers will be asked to increase the tax rate on carbon emissions to such an extent that carbon tax revenue will fall. Therefore, there is a risk that the use of a carbon tax to generate revenue could eventually create a perverse incentive to continue carbon emissions in order to provide a continued stream of carbon tax revenue. Using the Dynamic Integrated Climate Economy (DICE) model, we provide evidence that this risk is not a concern for the immediate future but that a revenue-generating carbon tax could create this perverse incentive as time goes on. This incentive becomes perverse at about year 2085 under the default configuration of DICE, but the timing depends on a range of factors including the cost of climate damages and the cost of decarbonizing the global energy system. While our study is based on a schematic model, it highlights the importance of considering a broader spectrum of incentives in studies using more comprehensive integrated assessment models. Our study demonstrates that the use of a carbon tax for revenue generation could potentially motivate implementation of such a tax today, but this source of revenue generation risks motivating continued carbon emissions far into the future.