It’s always controversial when the government comes to the rescue of private companies caught in a financial mess.

But in the case of mortgage giants Freddie Mac and Fannie Mae, the rescue plan proposed Sunday by the White House is vital for the economy.

Freddie Mac and Fannie Mae—the Federal Home Loan Mortgage Corp. and the Federal National Mortgage Association, respectively—were established to provide banks with liquidity to help more people buy homes.

The two companies hold about half the mortgages issued in the U.S. They don’t lend money to consumers, bu...