Quantifying climate change mitigation urgency seems to have three aspects:
(1) Green House Gas reduction targets required to meet a specific goal such as 2C.
The first guesstimate seems to be zero net emissions by 2050. **
**Until we actually have fully scalable carbon reduction technology we must assume zero emissions.
(2) Consequences to human society and the rest of life on Earth of exceeding the 2C goal.
The IPCC estimated impacts to crop yields seems quite significant.
(3) Estimates of the point of no return (tipping point) from feed back loops:
How much longer can we wait to begin climate change mitigation action before things such as the melting permafrost make climate change mitigation action infeasible?
Hypothetical answers to make the question more clear:
(1) If there is a consensus of agreement that we must achieve zero GHG emissions by 2050 this precisely quantifies one key aspect of the degree of urgency.
(2) If there is a consensus of agreement that business as usual for 80 years would probably cause 5C of global heating this is another quantified measure of urgency.
(3) If there is a consensus of agreement that 5C of global heating would very likely cause very significantly increased risk to things such as crop production yet another quantified measure of urgency.
(4) If we are 50 PPM of CO2 away from a key tipping point feedback loop such that the melting of the permafrost cannot be stopped this would provide another quantified measure of urgency.