I believe in it, because it's already happening. Air conditioners counter heat. Heaters counter the cold. The Venetians have proven that they can hold back storm surges, and live in a city slowly being flooded. The Dutch have proven they can hold back the ocean itself. We are capable of planting and harvesting crops on previously unfarmable land. Biodomes have been tested (and work) at a small scale, and show promise at their ability to scale up. We can desalinate and clean water at the cost of mere electricity - something we're making more and more abundant and less reliant on fossil fuels.
Moving from these technologies that exist today to live in a harsher world tomorrow is nowhere near as big a jump as curing cancer.
That doesn't strike you as a convenient thing to believe because it means not having to give up anything? You remind me of smokers 20 years ago who assured me that medicine would cure lung cancer before they caught it so they didn't worry about it.