In rough terms, I believe net CO2 sinks remove about 2 ppm of CO2 from the atmosphere annually, so if we cut global anthropogenic emissions to 0, CO2 PPM would fall by 2ppm per year. If we cut anthropogenic CO2 in half, it would fall by just 1 PPM per year. Obviously, this isn't going to lead to substantial changes in the short-term.
But that's really not the case politicians will or should make. The major gains from action on climate change are in avoided damages from long-term warming that does not occur thanks to near-term actions. Again, that's a really tough sell, as I hope my article and columns here have made clear. That's a large part of the reason why public support for carbon pricing is so small compared to the full social cost of carbon.
So I don't think the political sustainability of the policy really hinges on "how those "improvements" might be quantified over say a typical political term of 2-4 years in away that a politician could point to them and say "See what my administration did."" That's just not the kind of problem this is. Politicians will on the one hand need to convince people that this is a long-term endeavor that is worth undertaking. And then they need to link these near-term actions to near-term co-benefits of climate mitigation as best as they can to blunt the disconnect between climate mitigation costs and benefits. Finally, they'll need to do so in a way that doesn't run afoul of the various political economy constraints present (as discussed in Part 1 and 2 of this series).