There's a quote I admire, “Generals spend their careers preparing to fight the previous war.”
A little bit unfair to pick on the generals since this is really true of us as human beings; it's related to us expecting that the future will be a lot like the past, and often it's not.
CCL’s approach relies on government being strongly democratic. What's the point of lobbying a government that is not democratic? Answering my own rhetorical question, “not much.” I don't think it's an accident that the countries in the world that have their own CCLs, Canada, Germany, Sweden, are all fully democratic. That's a fraternity that the United States has fallen out of. My belief is the further we fall from being fully democratic, the less likely it is that CCL will have any impact. So that means in part for us here in the United States, working to get back to a fully democratic political system is every bit as important as working to mitigate the impacts of climate change.
The Economist is a solidly middle of the road and largely data-based publication. They publish an annual democracy index. You can see their findings from around the world here: https://en.wikipedia.org/wiki/Democracy_Index
While it's disturbing enough to think of the United States as a “flawed democracy,” for me it's even more disturbing to see the trend over the last ten years.
So to sum up my point, I think it's important, maybe even most important, that citizens concerned about climate change be working to bring US democracy back to health.