They're supposed to make it so anyone can get a home loan. Normally you need 10% down payment to even get looked at by a bank, but FHA loans (gubment) require 0-3.5% down. So more people buying houses equals higher prices.
Wikipedia says Fannie and Freddie owned 50% of the mortgage market in 2008. Any problems they had in 2008 were not insignificant, and that doesn't account for the influence on the market they had because of cheap/easy loans.

