back of the envelope, down and dirty calculations may help us here.
greenhouse gas would seem to cause the surface to be about 30C warmer than without GHGs. I have seen estimates for CO2 as being 5%-25% of the greenhouse gas effect. simple mathematical progression (1,2,4...128,256) put us into the 8th doubling from 1 ppm. atmospheric radiative calculations peg 2xCO2 at about 1C per doubling.
so 1C times 7+ doublings ~ 7C. 25% of 30C ~ 7C.
Therefore CO2 theory seems plausible if we make the assumptions that 1 ppm CO2 is the amount that causes the first 1C temp increase, that the GHG effect is 30C, and that CO2 is up to 1/4 of the GHG effect.
there are lots of uncertainties in those assumptions but I think we can safely say that CO2 does help warm the surface.
I am a lukewarmer, I think CO2 has an effect on surface temps. but I dont believe that there are net positive feedbacks that will multiply the 1C per doubling of CO2. I actually believe that the feedbacks will turn out to be net negative, especially in the long run.
why do I believe that? because H2O acts as both a heater and an air conditioner at the same time. when extra energy is around the air conditioner side runs more frequently (or earlier) and the extra clouds reflect solar insolation as they pump massive amounts of energy towards the TOA. the majority of the Sun's energy comes in at the equatorial region. ever wonder why ocean water never exceeds 30, 31 degrees Celcius? even though land often gets well over 40C?