The U.S. government's move to deepen its ties to mortgage-finance giants Fannie Mae and Freddie Mac by agreeing to absorb unlimited losses for the next three years is igniting a debate over whether it should bring the business operations of the companies onto its books.

A decision on how the government treats Fannie and Freddie could have broader political implications. So far, the White House has resisted calls by Republicans to bring Fannie's and Freddie's obligations onto the government's books, a move that could boost...