U.S. to Fund a $1.2 Billion Effort to Vacuum Greenhouse Gases From the Sky | Many scientists are skeptical of the technology, and environmentalists have criticized the approach.
Basically: you can do it, but for almost all applications, it's a lot cheaper to avoid burning fossil fuels than it is to remove CO2 from the atmosphere afterwards.
The problem is there's a few hundred billion tonnes or so that needs removing and it can't go from 0 to billions of tonnes per year overnight, but as soon as you start doing it publicly propagandists will flock to it and use it to delay more effective and pressing action.