Rush Limbaugh is claiming contrary to basic physics that "carbon in the atmosphere may actually be making things cooler, not warmer."
Limbaugh asserted that he was backed up by an article in The Economist, but the article actually examined how much the Earth is warming from emissions of carbon dioxide and other greenhouse gases, which by definition trap heat in the atmosphere.
The greenhouse effect is the reason that there is life on Earth, but since the Industrial Revolution humans have emitted billions of tons of carbon dioxide, trapping more heat in the atmosphere than the natural greenhouse effect would have. This warming has in turn set off several feedback loops that have on average amplified warming.
Climate scientists have studied the effects of different feedback loops, and in 2007 a consensus assessment by the Intergovernmental Panel on Climate Change found that the climate sensitivity of the Earth, or the amount that it would warm from a doubling of carbon dioxide, "is likely to be in the range 2°C to 4.5°C [about 3.5 to 8 degrees Fahrenheit] with a best estimate of about 3°C and is very unlikely to be less than 1.5°C." The Economist concluded that some recent studies indicate that "a small reduction in estimates of climate sensitivity would seem to be justified: a downwards nudge on various best estimates from 3°C to 2.5°C, perhaps; a lower ceiling (around 4.5°C), certainly."
Some of those studies are not yet peer-reviewed, some conducted by non-climate scientists, many are based on a model that has benefits but also limitations, and many do not take into account research suggesting the missing warming can be found in the oceans:
But even if climate sensitivity is found to be on the lower end of estimates, greenhouse gas emissions are outpacing our worst case scenarios, meaning warming by the end of the century could still end up "exceed[ing] the adaptive capacities of many societies and natural systems," as a 2013 World Bank report put it. Due to this, the International Energy Agency has warned that without "stringent new action" warming will exceed 2 degrees Celsius (3.6°F). Limiting warming to 2 degrees Celsius as we committed to, would still raise sea levels to points that would threaten the existence of many island nations.
And even if climate sensitivity is found to be on the high end of estimates, Limbaugh will still deny manmade global warming entirely. After all, every investigation in the "Climategate" controversy -- including one that Fox News had touted as the "final say" in the matter -- cleared climate scientists of falsifying data. Yet Limbaugh is still citing "Climategate" to claim that global warming is a "hoax."