That's a misrepresentation of the evidence. I'm a layman, so anyone reading should offer any necessary correction.

Carbon dioxide is a greenhouse gas. So is water. There is enough water around that we probably misnamed the planet, and in general we can say that the atmosphere is saturated with it: you may even have noticed some precipitation.

Between CO2 and H2O and a few other things, our planet is kept temperate instead of being a ball of ice. For the most part, water completely swamps the effect of CO2, and for the most part, the atmosphere is completely opaque to outgoing radiation at far lower levels of CO2 than are present naturally. So we can ignore CO2, right? Almost. There is a small window of radiation that water vapor does not block, but more importantly, there is not a lot of water above the troposphere.

IR photos look blurry. The mean free path of an IR photon (which is how most heat leaves Earth, because Planck) at sea level is quite short, in the tens-of-meters, with the distance rising as the photon makes its way out of the atmosphere. The radiative top-of-atmosphere is where the mean free path becomes infinite. The effect of an increased partial pressure of CO2 is to push the CO2-dense layer further out into space. Outgoing radiation must take a longer path to reach space, and therefore we say that this traps heat near the surface. The effect is not large: the commonly accepted figure is 3.7 W/m^2 per doubling of CO2, which is usually held to be equivalent to about 1 degree of global temperature.

If there were no other considerations, we would probably be justified in ignoring CO2-induced warming indefinitely. However, as any resident of the American South will attest, there is a pretty wicked relationship between temperature and humidity. Warmer air can hold exponentially more water vapor, and it's not a gentle exponent. A naive calculation would suggest that the CO2-H2O feedback loop would result in arbitrarily high temperatures. Fortunately this is not observed, but the lower bound for warming is pretty hard, due to thermodynamics, and at least part of the H2O feedback is strongly positive. We are in for some warming, any way you dice it.

But hey, that could be anyone's CO2, right? Well, no, not really. We know how much oil we're burning, and petrocarbon has a very different C13 ratio than what we find in the rest of the carbon cycle, and we're completely dwarfing the volcanic CO2 output. There's a T. Gerlach of USGS who has given humanity's output of CO2 as about one Pinatubo per day, or one or more Yellowstone-sized supervolcano eruptions per year. By volume, this is not the worst outgassing the planet has seen. The Deccan Traps released something like 1000 times the amount of carbon that humanity has managed to liberate. However, that took a few million years, and we are on track to equal that outgassing in about 1000 years at the current rates.

"But," you say, "how do we know there isn't some alternate explanation?" We cannot rule out new physics. However, new physics has to reproduce the results from the old physics. We know that CO2 and H2O are greenhouse gases, and we know we need a very large effect to counteract them, because at least part of the feedback loop is strongly positive. Despite the efforts of Dr. Lindzen, it seems we can rule out clouds as a moderating influence. A large unnoticed way to transfer energy to space is pretty implausible at this point, and it still would leave us with a CO2 problem in the long run; there are limits even to special pleading.

The explanation of global warming is complex, but not as complex as trying to model the future effects. There is a great deal of effort devoted to conflating these two things for political purposes.