Bill rolled out by House GOP last week would eliminate Fannie and Freddie and modify qualified mortgage regulations.
Thursday hearing will focus on secondary mortgage market reform bill.
Trade group says it does have some concerns while California Democrat says bill is partisan ideology and another attack on middle class.
GOP-backed measure would create the "National Mortgage Market Utility" regulated by FHFA.
Proposed rule adds some exemptions to Dodd-Frank requirements set to take effect next January.
FHFA says more than 2.5 million housing finance loans have now been done through HAP since 2009.
Sallie Mae chief responds to criticism earlier this week from Sen. Elizabeth Warren (D-Mass.)
Senate gets measure Tuesday that would shut down Fannie Mae, Freddie Mac and FHFA within five years and create new corporation similar to FDIC.
Not much impact seen from Fannie Mae, Freddie Mac decision to buy only qualified mortgages after Jan. 10, 2014.
FHFA said the GSEs will generally not buy loans that don't meet the CFPB's new "ability to repay rule."