Though growth and housing availability are connected, one doesn't necessarily cause the other, according to this post on The New York Times' Economix blog.
"Booming Sun Belt cities - Atlanta, Phoenix, Miami, Las Vegas, Tampa - had the most extreme combinations of high prices and oversupply. Houston and Dallas also built plenty, but their prices stayed earthbound and as a result, they don't seem to have overbuilt. Coastal America had booming prices, but regulatory and natural limits on building restricted construction. And now we see the sharpest declines in the rate of population growth in places that had the most overbuilding.
The four states where population growth fell most in 2009, relative to statewide trends in 2000-8, were Arizona, Georgia, Nevada and - above all - Florida. These are not the states with the worst economic conditions today. (California and Michigan have that honor.) They are, however, places that had particularly extreme housing booms - measured by both quantities and prices. No one should be surprised that their population growth rates have fallen furthest."