Global warming is caused by carbon dioxide and methane emissions. It is not at all the same as the pollution which has citizens wearing masks in Chinese cities -- that is what used to be called 'conventional air pollutants': particulates, carbon monoxide, sulfur dioxide, nitrogen oxides, and hydrocarbons heavier than ethane. These are a lot easier and cheaper to scrub from industrial and power plant gas emissions than carbon dioxide is. Remove them, as we largely have done, and the carbon dioxide emissions remain. Methane as well.
Yes, as the name implies global warming is a global problem. Our greatly reducing, even eliminating, our carbon dioxide emissions will accomplish little if the rest of the world fails to do the same. China already emits more carbon dioxide than we do and didn't agree at Paris to even stop increasing their emissions until 2030. Clearly this isn't satisfactory. Clearly we don't want to lose our manufacturing and ship it to China, where carbon dioxide emissions per unit of production are higher than if the product were manufactured in the United States.
Of course we don't want to destroy our own or the world economy in fighting global warming. That is why a reasonably attainable target year to achieve a significant reduction in global warming gas emissions is needed. Wrecking economies leads to political instability, which can lead to war. We don't want to replace global warming with nuclear winter.
However if carbon dioxide emissions keep increasing, the worsening of global warming is going to create problems which we cannot satisfactorily mitigate, either here or around the world. Around the world matters, because severe global warming is going to cause extreme mass migrations, which also likely lead to war.
The goal is not to reduce the global temperature. It is to limit the future rise to another 1 or 2 degrees F. We are already reaching the point where that may be unattainable.
I also see natural gas as a transition fuel, as we move away from coal and oil. We can be fossil fuel independent with solar, wind, geothermal, hydropower, and nuclear progressively replacing fossil fuels. That need not damage our economy.