The climate change debate really isn't about the basic science of greenhouse gases. Just like physical actions can cause a mechanical system to vibrate, the frequencies that the molecular bonds of CO₂ can absorb and vibrate to are in the infrared spectrum, what we measure as heat. No scientist argues that.
All else being held equal, under laboratory conditions, each doubling of the CO₂ concentration in a gaseous mix under infrared light spectrum (the part of the spectrum that is felt as heat) will increase the temperature of that gaseous mix by about 1.1°C (which is about 2°F). That would mean that in order to go up by that 1.1°C the concentration would have to go from the approximately 280 ppm (parts per million) of the 1800s to 560 ppm. To go up another 1.1°C we would have to double that, to 1120 ppm. For a third 1.1°C increase it would take going up to 2240 ppm. We're currently at 400 ppm, less than halfway to even a first doubling.
The disagreement is actually about the multipliers that fuel the "catastrophic" story line. Because all else in the chaotic system that is a worldwide climate system is not held equal. Any initial change creates secondary changes. The question is what those secondary changes are and do they, on balance, tend to increase the temperature further or to reduce the overall temperature changes and by how much.
The catastrophe predictors use a multiplier as much as 6 or more, meaning that each doubling would make the temperature go up by 6.6°C. Even the IPCC (The UN's Intergovernmental Panel on Climate Change) has reduced the low end of their expected targets to a multiplier of only 1.5. However, actual readings of temperature suggest an even lower multiplier because what's being measured is lower than 95%+ of the all various computer models' projections.
While there is consensus (and even if there weren't it wouldn't matter - science is what it is and scientists make mistakes regularly) on the basic science of greenhouse gases, there is *no* consensus on the magnitude of the feedback mechanisms or even what all the feedbacks are. We're continually finding new ones. We're also continually finding new cycles and other things that affect the climate in general, everything from the sun to cosmic rays, ocean currents and many others that also come into play in the net climate at any given time.
We can't even explain much of the known climatic changes in the past. It's the height of hubris to say we know what it will be 100 years from now. We can't even predict the totally human created stock market using computers. How on Earth (pun intended) can we predict the far more chaotic changes in a global climate?
But by the same token, to deny basic physics isn't good either. Yes, CO₂ does affect atmospheric temperature. But the net human and natural consequences of those changes aren't known. We know it improves some things, particularly plant growth and the fact that more people die from cold related illnesses and injuries than heat related. Others it may make worse such as the rate of sea level rise (the sea level has been rising since the last ice age ended - it's just somewhat faster now).
In the even longer range, we may actually *want* to do everything we can to increase the average temperature as we approach the end of this interglacial period. We're already past the time period that some of them have lasted before cooling to a new ice age again.