Global policy targets for greenhouse gas emissions reductions are being negotiated. The amount of emitted carbon dioxide remaining in the atmosphere is controlled by carbon cycle processes in the ocean and on land. These processes are themselves affected by climate. The resulting 'climate–carbon cycle feedback' has recently been quantified, but the policy implications have not. Using a scheme to emulate the range of state-of-the-art model results for climate feedback strength, including the modelled range of climate sensitivity and other key uncertainties, we analyse recent global targets. The G8 target of a 50% cut in emissions by 2050 leaves CO₂ concentrations rising rapidly, approaching 1000 ppm by 2300. The Stern Review's proposed 25% cut in emissions by 2050, continuing to an 80% cut, does in fact approach stabilization of CO₂ concentration on a policy-relevant (century) timescale, with most models projecting concentrations between 500 and 600 ppm by 2100. However concentrations continue to rise gradually. Long-term stabilization at 550 ppm CO₂ requires cuts in emissions of 81 to 90% by 2300, and more beyond as a portion of the CO₂ emitted persists for centuries to millennia. Reductions of other greenhouse gases cannot compensate for the long-term effects of emitting CO₂.