"In his first year in office Reagan halved the budget for public housing and Section 8 to about $17.5 billion. And for the next few years he sought to eliminate federal housing assistance to the poor altogether."
From the Wikipedia article entitled "Public housing in the United States", which has a section specifically about the period of time in question:
"Under the Reagan administration, household contribution towards Section 8 rents was increased to 30% of household income and fair market rents were lowered. Public assistance for housing efforts was reduced as part of a package of across the board cuts."
I am not an American and don't know the history of American federal program funding, but I do have access to things that let me search for things. You should try it.
http://www.cato.org/pubs/pas/pa127.html
#Edit. Reading the article further, it seems the Cato institute dismisses/rebukes most of the points regarding federal housing being the cause of homelessness in the 1980's.
From the link:
Like the shift from 40-year mortgage subsidies to 15- year housing certificates, the shift from the certificates to 5-year vouchers enabled Congress to reduce HUD's budget authorizations. Such reductions have created the mistaken impression that federal housing assistance has been cut. In fact, annual outlays increased from $5.7 billion in 1980 to $13.8 billion in 1988. The number of families being served by HUD housing programs rose from 3.1 million in 1980 to 4.2 million in 1988. Moreover, a housing voucher costs the government only about $4,500 a year, whereas a new unit of public housing costs it $9,000 a year.
I guess mistaken impressions are still common on the internet.