Decision-makers have confirmed the long term objective of preventing a temperature increase greater than 2 °C. This paper aims at appraising by means of a cost-benefit analysis whether decision makers’ commitment to meet the 2 °C objective is credible or not. Within the framework of a cost-benefit type integrated assessment model, we consider that the economy faces climate damages with a threshold at 2 °C. We run the model for a broad set of scenarios accounting for the diversity of “worldviews” in the climate debate. For a significant share of scenarios we observe that it is considered optimal to exceed the threshold. Among those “non-compliers” we discriminate ”involuntary non-compliers” who cannot avoid the exceedance due to physical constraint from ”deliberate compliers” for whom the exceedance results from a deliberate costs-benefit analysis. A second result is that the later mitigation efforts begin, the more difficult it becomes to prevent the exceedance. In particular, the number of ”deliberate non-compliers” dramatically increases if mitigation efforts do not start by 2020, and the influx of involuntary non-compliers become overwhelming f efforts are delayed to 2040. In light of these results we argue that the window of opportunity for reaching the 2 °C objective with a credible chance of success is rapidly closing during the present decade. Further delay in finding a climate agreement critically undermines the credibility of the objective.