MCLEAN, Va.—When Charles E. Haldeman Jr. became Freddie Mac's chief executive officer in August, the ailing housing-finance giant had already consumed $51 billion of government money to stay afloat. It's likely to need even more.

Freddie's federal overseers nevertheless have instructed Mr. Haldeman to focus on something that isn't likely to make the bleak balance sheet look any better: carrying out the Obama administration plan to allow defaulted borrowers to hang onto their homes.

On...