Can't speak for the community at large.

CO2 blocks some frequencies of infrared. This is known and uncontested by even the craziest deniers. Without an atmosphere the earth's average temperature would be around -20 C. You can calculate this based on radiation theory. (that specific number may be wrong, but it's around there). An atmosphere with CO2 (and some other major ones I don't remember) blocks a higher proportion of the radiation from earth than from the sun (because the earth radiation is mostly infrared near the range blocked by CO2). With a model for that, you can recalculate the surface temperature. It will be much higher.

edit: (on the other hand, now that I think about it, I can't prove to myself that absorbant CO2 will actually cause a greenhouse effect. Maybe it's reflective, which would cause greenhouse...) /edit

edit2: ok I just read the wiki article. Everything they tell you about how the greenhouse effect works is wrong. It's not that the atmosphere somehow blocks the outgoing radiation, as that would violate the second law by allowing the earth to heat up relative to it's surroundings. The real mechanism is that the absorbtion surface (the ground) and the emission surface (roughly tropopause) is seperated by a mechanism that enforces a temperature difference (adiabatic lapse rate). I need to think about this more. /edit

That analysis does not include things like the effect of temperature on albedo (clouds and snow), which changes things, and other effects, but it gives you rough bounds for what must happen. The model establishes a causal link from CO2 to temperature (there are also links the other way, like forest fires and desertification).

Beyond that, though, climate science is mostly empirical I think.

My rough belief is that global warming is a thing, but is probably hyped up a bit too much for political reasons.