An article from the Associated Press, STUDY: 35 PERCENT IN US FACING DEBT COLLECTORS, cites a study by the Urban Institute. The article states:
The study found that 35.1 percent of people with credit records had been reported to collections for debt that averaged $5,178, based on September 2013 records.
The article also notes:
[The Urban Institute] figures nearly match the 36.5 percent of people in collections reported by a 2004 Federal Reserve analysis.
Unfortunately I could not find in short order either the Urban Institute or Federal Reserve studies referred to.
It is not clear from the article whether 35% of Americans are currently in collections, or have at some point been in collections (and if it is at some point, how far back these statistics account for).