http://www.census.gov/ipc/www/img/worldpop.gif
According to the US census department by 2050 we will be approaching 10 billion, I figure 12. By 2100 20 billion.
Now you are talking about 6000 square feet for each person the population just fitting into the southern states.
Not to mention that it takes several acres to supply enough food to feed each of those people you have huddled together in 6000 square feet.
But more to the point. If we are starting to see the effects of global warming with a population of 6 billion and we have only been between 3 and 6 billion for only 50 years. That means that the effect we are having on the environment is more pronounced now.
In other words even at current population we are still talking about a very quick impact on the environment. 50 years at current levels would yield more catastrophic change then the last 50 years. In fact we would need to produce less CO2 then environment can absorb in order to counter act the current levels of CO2. 3 billion people might even be too much for that.
But unchecked by 2050 we are likely to be from between 10 and 12 billion strong. Even with that 25% reduction in use of fossil fuels we still will be producing more CO2 than today. (1.5X more)
If we reduce co2 emissions by 50% we will still be having a cumulative effect on the environment.