Last I looked the US were still below 1% of the population being incarcerated (~0.7% total, ~0.9 adult). This is (or was, there may be newer figures) the world's highest rate.
These numbers are disgusting (especially considering the number of people in US prisons purely because they can't afford to post bail), but I think it would take substantially higher rates to cause the collapse of a country.
The detriment of a country is a completely different matter, and this situation in the US is already recognized by most of the rest of the world.
Similar issues are being seen in China and Russia.
From http://news.bbc.co.uk/2/shared/spl/hi/uk/06/prisons/html/nn2... (which is probably well out of date by now):
"Half of the world's prison population of about nine million is held in the US, China or Russia.
Prison rates in the US are the world's highest, at 724 people per 100,000. In Russia the rate is 581."