GOP panel members anxious to move measure along while Democrats ask to wait until after recess to allow public input.
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.
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.
House Financial Services hearing features partisan back-and-forth over Fannie and Freddie.
The bulk of credit union and CUSO mortgage programs will see minimal impact from Fannie Mae and Freddie Mac limiting the secondary market to only qualified mortgages, according to credit union and CUSO executives.