Why doesn't natural gas count? It's increased usage is one of the key reasons the US's carbon output is down over 10% since 2005.
> "There are two basic factors that have contributed to lower carbon intensity (CO2/kilowatthour [kWh]) in the electric power sector: 1) substitution of the less-carbon-intensive natural gas for coal and petroleum, and 2) growth in non-carbon generation, especially renewables such as wind and solar."
It's impossible to win with converting a fossil fuel X into something and then to convert back to fossil fuel X, because of basic thermodynamics. If you want to convert fossil fuel X to something to convert to fossil fuel Y, you may be able to "win" over the current situation but you will very likely never get to get zero emissions in the system as a whole, because of the first step. It isn't necessarily impossible to burn X tons of CO2 and pull X+delta tons of CO2 out of the air, depending on the exact binding energies of the chemicals involved (which given that both are fuels, probably don't have an advantageous difference you can exploit), but you'll certainly be paying somewhere else to do it. And given that pulling CO2 out of the air at scale is quite challenging even on its own merits, it probably can't win in a practical manner.
If you're going to pull CO2 out of the air you pretty much have to be using a non-CO2-generating power source to do it if you want to net CO2 withdrawal.
> "There are two basic factors that have contributed to lower carbon intensity (CO2/kilowatthour [kWh]) in the electric power sector: 1) substitution of the less-carbon-intensive natural gas for coal and petroleum, and 2) growth in non-carbon generation, especially renewables such as wind and solar."
http://www.eia.gov/environment/emissions/carbon/