We already have this technology, they're known as CO2 scrubbers.

I have a bad memory but I seem to recall Sergey Bring or Larry Wall or someone "important in technology" saying that this is basically already a solved problem -- heavily investing in to CO2 scrubber technology, hooking the things up via solar, and deploying them across the world's deserts -- but that todays problem is that leadership problem you mentioned. No one (Government) wants to foot the bill.