Everybody acknowledges that carbon dioxide only takes the tiniest sliver of infra-red radiation, and that there is sufficient amounts now in the atmosphere to make that spectral band completely opaque. In order to make carbon dioxide more relevant, they must invoke 'positive feedback'.
That means the earth is horribly unstable, in terms of CO-2. In other words, a little rise carbon triggers other massive effects. For example, the frozen methane in ocean sediments bursts out. Or ice sheet melting changes the ocean currents. Or there are significant changes in the upper atmosphere.
The latest speculation says that isostatic rebound (crust rising) will trigger massive volcanoes, which will further increase global warming. Of course, if the earth were really that unstable, we might not even be here.
I once listened to a famous professor give a talk on the carbon-water cycle in the past billion years, or so. Atmospheric water is a zillion times more powerful than carbon, but nobody says much on this, other than to invoke more instability (carbon increases water, etc). Anyway, these levels have gone up and down like a toilet seat, over geologic time. Mankind is a mere pimple on a flea, on this timescale. (I think this will be a good boring story!)
I'm not saying anything against all this stuff, since I would probably get a letterbomb or something, but I do find it interesting....