Green Keynesianism seeks to wed the policies of economist J. M Keynes, which focused on heavy state investment to stimulate growth, with the incredible costs needed to transition to a sustainable economy. Keynesianism is a theory of demand-side economics, positing that economic growth and full employment are sustainable in a system where there is adequate demand. Where there is high unemployment there is low demand, because consumers do not have money to spend. Keynes suggests that government investment can generate demand for goods and services where the market stagnates through investment and infrastructure projects which create jobs.  The idea of "greening" Demand-side economics developed around the time of the 2008 financial crash, rising to prominence in 2018. 
The potential costs of transitioning to a sustainable economy are enormous, but the costs of doing nothing will be greater. Keynesian models rely on huge public spending to create jobs, increase consumption and stimulate growth. This growth is used to offset the cost and debt accrued from massive public spending. In these terms, Green Keynesianism is a win-win: it promises to create jobs while building the sustainable infrastructure we need.
To be effective, Green Keynesianism would be very expensive. The American Action Forum, a Centre-Right think tank, puts the cost of a US Green New Deal at $93 trillion - quadruple the US' current level of debt and nearly five times its GDP . This level of public borrowing would be unprecedented and may lead to spiralling debt and government insolvency. Critics from the left may argue that the Green New Deal does not solve the problem at the heart of the climate crisis, the fallacy of infinite growth on a finite planet. As soon as the Green New Deal fails to produce growth - which it must eventually do - it will collapse.  There are also practical issues with the Green New Deal. Renewable Energy Sources require land, and energy to produce. Britain would need to cover 30% of its landmass to meet its energy requirements with solar panels. They also require the extraction of high quantities of earth minerals to produce.
Rejecting the premises