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.