Quantifying CO2 generated/released by the soft drink industry and breweries
The xkcd What If? blog, by Randall Munroe, addressed a similar question.  He states the result better than I can.


  For most of the history of civilization, there were about 270 parts
  per million of carbon dioxide in the atmosphere. In the last hundred
  years, industrial activity has pushed that number up to 400 parts per
  million. 
  
  One "part per million" of CO2 weighs about 7.8 billion tons.
  A can of soda contains in the neighborhood of 2.2 grams of CO2, so you
  would need about 450 quadrillion cans of soda. That's enough to cover
  the Earth's land with ten layers of cans.
  
  
  Randall Munroe - xkcd What If? #88:Soda Sequestration. http://what-if.xkcd.com/88/
  


For further perspective, each breath of a healthy adult male involves about 500mL of gas exchange.  The air is, on average, 0.04% CO2 prior to inhaling.  Exhaled air contains between 4 and 5 percent carbon dioxide, I'll call it 4.04% for a nice, round 100-fold addition.  The mass of 500mL of air is about 0.6g, and though it will be slightly more dense with the added carbon dioxide, I'll assume that it remains at that mass for simplicity's sake.

So 4% of the 0.6g is CO2 that was added to the atmosphere by a single adult male breath.  That's 0.024g.  About 90 breaths add as much CO2 to the atmosphere as the carbonation in a can of Coke.  Where does the additional carbon in those breaths come from?  The Coca Cola itself, of course.

The sugar in the can of Coke (39g) contains about 16g of carbon atoms.  After being metabolized, that turns into 57.2g of carbon dioxide.  Not considering any of the energy required to harvest, process, or transport the sugar, that's still 26 times a much carbon dioxide going into the atmosphere from the calories in a can of Coke as opposed to its carbonation.  

To put it more succinctly, the CO2 output from the carbonation in Coke could be completely offset by reducing overall caloric intake by 6 calories per can.