Wind whistles through window casings, elevators fail, roofs leak, mold metastasizes -- and Mayor Bill de Blasio is scrambling for ways to close a nasty $13-billion shortfall in the maintenance and repair budget for the New York City Housing Authority.

The situation is critical. Washington has sharply scaled back its support for NYCHA. Between 2001 and 2013, Congress underfunded the public housing agency by nearly $1 billion. Today 70% of its buildings are more than 40 years old and deteriorating -- while most of its 400,000 residents live in substandard conditions.

So now de Blasio and NYCHA chief executive Shola Olatoye are searching for surefire moneymakers. One idea in particular stands out. The mayor is considering a plan to put a tax surcharge on residences valued at $5 million and up that are owned by part-time New Yorkers.

The Fiscal Policy Institute, a union-supported research group, reckons the plan could bring in $665 million a year. That wouldn't plug the NYCHA repair deficit, but it could dramatically narrow the gap.

The Partnership for New York City, a business group, says the idea could work if it's placed in a larger tax-reform package that eases the burden on small businesses. That argument is reasonable. Small businesses often take the first hit when neighborhoods go upscale. While some business and real estate organizations think the proposal might tax the superrich out of the city, that notion seems unlikely.

Nothing is in writing yet, but the plan would likely apply to apartment owners who are out of the city at least 183 days a year and pay no NYC income taxes. Most still use plenty of municipal services. And the money should be in a locked box for NYCHA.

Should de Blasio put a decent plan on the table, it would still have to clear Albany before it becomes law, and the State Senate might be a tough sell next year. But as Washington backs out, the city doesn't have the money to support NYCHA alone. So the agency is left without a sustaining partner -- and way too many New Yorkers are left ill-housed. That is not acceptable.