WASHINGTON (AP) — Homebuyers could feel the pinch if Congress follows through on plans to shut down Fannie Mae and Freddie Mac, the government-controlled mortgage guarantee giants that were rescued by a $187 billion taxpayer bailout during the financial crisis.

Borrowers would probably end up paying slightly higher mortgage rates under House and Senate bills that would phase out Fannie and Freddie over five years and shrink the government’s huge role in guaranteeing mortgage securities. Fannie and Freddie teetered under a crush of massive losses on risky mortgages before being bailed out.

The House Republican bill would virtually privatize the mortgage market. The Senate’s bipartisan plan envisions a continued but more limited government role in insuring mortgage securities. Supporters say that would keep mortgages available and affordable.

Congressional efforts to overhaul the nation’s mortgage finance system got a boost Tuesday from President Barack Obama’s call for changes that are generally in line with the Senate’s bipartisan plan.

“For too long these companies were allowed to make huge profits buying mortgages, knowing that if their bets went bad, taxpayers would be left holding the bag. It was ‘heads we win, tails you lose,’ and it was wrong,” Obama said. “The good news is right now there’s a bipartisan group of senators working to end Fannie and Freddie as we know them. And I support these kinds of reform efforts.”

The idea behind both plans is to shift more mortgage financing risk from the government to the private sector to prevent taxpayers from having to pay for future bailouts. But there’s a price homebuyers would likely pay for having private investors shoulder more risk to protect taxpayers.

“It will mean higher mortgage rates,” said Mark Zandi, chief economist at Moody’s Analytics. “The question is how much higher.”

Typical borrowers could pay about $75 per month in extra interest payments, about half a percentage point, on an average mortgage under the Senate proposal, Zandi estimated, and about $135 more under the House plan. That’s on a conforming loan of about $200,000 with the borrower providing a 20 percent down payment.