Part of the economic recovery plans implemented by governments following COVID-19 is directed towards the energy transition. To understand the potential effects of these post-COVID green recovery packages on reductions of greenhouse gases emissions, we investigated three different approaches. Firstly, we analysed simulation results of Integrated Assessment Models (IAMs) to infer the change in CO2 intensity of GDP that could result from post-COVID low-carbon investment plans. Secondly, we investigated the scenarios provided by the International Energy Agency (IEA) based on a bottom-up energy system model. By combining the two approaches, we found that green recovery packages implemented and planned globally can lead to an emission reduction of merely 1%-6% from 2030 baseline levels at most. Thirdly, we looked into the results of the Adaptative Regional Input-Output model, which simulates the dynamic effects of economic crisis and fiscal stimuli through supply chains following labour shortage. The third approach shows that the increase of activity driven by fiscal stimuli leads to a rebound of CO2 emissions even if they do not target carbon-intensive sectors. We conclude that green recovery packages targeting low-carbon technologies have a limited impact on near-term CO2 emissions and that demand-side incentives, as well as other policy efforts to disincentivise the use of fossil fuels, are also important for scaling up climate mitigation.