There has been a lot of research in the economics of climate mitigation. See also related question here, which alas focused on what the most cost-effective solution might be, a very difficult question.
And of course politicians have made sound-bite claims from all that. I'm not sure if that can be said to have been well articulated. For example, a paper on this on UK political discourse concluded:
Corpus analysis, a method developed within linguistics, is used to investigate how UK politicians talk about climate change, using the example of the 2008 Climate Change Bill. [...] The analysis shows that politicians frame climate change as an economic and technical issue, and neglect discussion of the human and social dimensions. They are selective in their use of scientific evidence, with little mention of abrupt or irreversible change. In doing so, they attempt to ‘tame’ climate change, rather than confronting difficult realities. While this strategy has the benefit of political acceptability, it does not allow for discussion of the full political and social implications of climate change, and precludes more radical responses.
And the UK is quite relevant, because it issued the Stern report, which was influential in framing the discussion elsewhere as well
In the late 2000s, the UK Labour Government made a conscious choice to frame climate change as a discussion about economics, with the publication of the government-commissioned Stern Report in 2007. Stern, an academic economist and government adviser, presented climate change as a ‘market failure’, and estimated the monetary costs and benefits of climate action (Stern 2007). Though controversial, this approach won the support of business groupings and helped to build the cross-party support which contributed to the successful passage of the Climate Change Act (Carter and Jacobs 2014). The Labour administration’s strategy can be seen as part of a wider trend towards using economic language and policy instruments to achieve environmental goals, termed ‘ecological modernisation’ (Hajer 2000).
The part of the Stern report which dealt with the costs of mitigation was probably even more argued over than the consequences for doing nothing.
So, whether the costs for various mitigation measures have been clearly laid out to the general public, I'm not sure, but I suspect not given the first quote.
Some researchers argue that given the limitations of the cost-estimation methods (in relation to expected results), costs should not even be an issue that is emphasized.
The IPCC 4th assessment, as summarized in Wikipedia gives these cost estimates:
The IPCC estimates that stabilizing atmospheric greenhouse gases at between 445-535ppm CO2 equivalent would result in a reduction of average annual GDP growth rates of less than 0.12%. Stabilizing at 535 to 590ppm would reduce average annual GDP growth rates by 0.1%, while stabilization at 590 to 710ppm would reduce rates by 0.06%. There was high agreement and much evidence that a substantial fraction of these mitigation costs may be offset by benefits to health as a result of reduced air pollution, and that there would be further cost savings from other benefits such as increased energy security, increased agricultural production, and reduced pressure on natural ecosystems as well as, in certain countries, balance of trade improvements, provision of modern energy services to rural areas and employment.
The IPCC considered that achieving these reductions would require a 'large shift in the pattern of investment, although the net additional investment required ranges from negligible to 5-10%'.They also concluded that it is often more cost effective to invest in end-use energy efficiency improvement than in increasing energy supply.
And long-term
Among the measures that might be used, there was high agreement and much evidence that policies that put a price on the cost of carbon emissions could provide incentives for consumers and producers. Carbon prices of 5 to 65 US$/tCO2 in 2030 and 15 to 130 US$/tCO2 by 2050 are envisaged for stabilization at around 550 ppm by 2100.
As you can seen, that's a pretty wide interval of costs...
In Europe, where climate change is generally accepted as a real problem, the EU has put out various press releases on how much they plan to budget for it in monetary terms. How much they expect to achieve with that in terms of actual CO2 reductions is usually not said in such contexts... On the flip-side, Merkel has pledged to make Germany carbon neutral by 2050, but the costs of achieving that don't seem to get touched in the media coverage of the initiative. Likewise for the French initiatives. Wikipedia has a pretty long article on the German Climate Action Plan 2050, but costs are hardly mentioned, except perhaps in the criticism section as "minimum price on carbon is also missing completely". The plan does talk, in general terms, of potentially raising some taxes. But most of it seems to consist of emission targets per economic sector; these targets don't come with a cost estimate (at least in Wikipedia's presentation).
