The squeeze comes when there is no more clean water...just because there's lots of vacant land in the desert doesn't mean this land could automatically become fertile with the addition of water...it's a desert for a reason. Water is becoming scarce in many parts of the world, drought is increasing and we are depleting our aquifers. (Personally, I had my tubes tied after two kids.)
Everyone here with some science training knows that exp(a t) becomes insanely large as t increases if a > 0. That means that unless we found a way of caring for exponentially more people for the indefinite future, we are in trouble at some point. Even Moore's Law has run out - at least for CPU clock speeds.
Following that logic through, the exponential population growth will end at some point, and there are good ways to end the growth, and really horrible ways for the growth to end. My argument is that if we put our heads in the sand and pretend the population growth can continue indefinitely, we (or rather those who come after us) will encounter the horrible limit to population growth.
Talking about limiting population growth maybe sounds inhumane to some, but I think quite the opposite. I don't want billions of people to starve - even in the future - I want the human population of the Earth to continue for a long time (hey, we might get reincarnated!).
As regards greening the Sahara (I have seen suggestions that the extra CO2 in the atmosphere might help that process), I'd like to see that used to make life better for the people we already have on the planet, not used as an excuse (before it has even happened) to ignore the relentless increase in our population.