The D.C. government is embroiled in a much-publicized dispute over the future of about 300 homeless families at the notorious shelter at the former D.C. General Hospital.

But that predicament — as serious as it is — is minuscule compared with the District’s related challenge of providing reasonably priced housing for low-income households in which people have a place to live but face severe problems covering the cost.

Their number exceeds 50,000, and many worry their next step is homelessness if rents and home prices continue to rise.

For both the District and the suburbs, the shortage of affordable housing looms as one of the principal threats to the region’s quality of life and economic competitiveness. It hurts janitors and school teachers, young professionals struggling with student debt, and the restaurant waitresses who serve them.

It’s also one of the hardest problems to tackle, partly because the projected cost runs in the billions of dollars as gentrification and other market forces drive up rents and home prices in many neighborhoods.

Now, a group of local leaders representing government, business and the philanthropic sector is studying whether to propose a “regional compact” in which the Washington area as a whole would commit to addressing runaway housing costs.

If nothing is done, they warn, the problem of overpriced housing will fester until it eventually explodes into a widely recognized crisis — much as the Metro transit system’s problems were ignored for years until they recently triggered a burst of attention.

The committee, called the Greater Washington Housing Leaders Group, was established two years ago. Its founders include representatives of the Metropolitan Washington Council of Governments, Citi Community Development and the Washington Regional Association of Grantmakers.

So far, the group has collected data about the region’s housing, examined possible solutions and made presentations to local groups including officials in Prince George’s and Montgomery counties.

Recently, it plunged into the hardest part of the task: putting a dollar figure on what it might cost the region to achieve a genuine solution, and picking specific steps to do so. These would include a mix of more public and private investment and changes in zoning rules and other policies.

They probably also would include a public compact, or pledge, in which the District and surrounding counties would each commit to produce its fair share of affordable housing over a specific period. Otherwise, there’s a risk that each jurisdiction would hope that its neighbors would pick up the burden — a pattern that has been an obstacle in the past.

At a presentation to Leadership Greater Washington on Tuesday, the group said the region needed to summon the political will to curb overpriced housing, while warning that the cost would be high.

Early estimates are that the total cost of new, affordably priced housing would be in the tens of billions of dollars, and the necessary government subsidy would run in the billions.

Much of the public cost would probably help fund construction or preservation of affordable housing and provide subsidies and other help for renters. This would partly offset steep declines in federal government support in recent years.

“We’ve got to stop having these million-dollar conversations about billion-dollar problems,” said David Bowers, vice president of Enterprise Community Partners, a nonprofit organization and one of the group’s founding members. “If we don’t act, the problems will only get worse, as we’ve seen with Metro.”

To get a sense of the scale of the problem, consider this: D.C. Mayor Muriel E. Bowser (D) has drawn praise for pledging to add at least $100 million a year to the city’s Housing Production Trust Fund.

But that commitment doesn’t go far. In January, she said an $82 million allocation from the fund would pay to create or preserve more than 800 units of affordable housing.

That works out to about $100,000 per unit. At that rate, providing affordable housing for more than 50,000 overstretched households in the city would cost upward of $5 billion.

Naturally enough, the poorest people are those most affected by high housing costs. A survey in April in the District found that finding and keeping affordable housing was by far the dominant stress among the lowest-income residents — those receiving the equivalent of $24,300 or less for a family of four. In that group, nearly 3 in 5 worried about losing housing altogether.

But housing prices are a major problem for lower-middle-class people as well. One of the housing leaders group’s key findings has looked at households with total income up to the equivalent of $70,150 for a family of four.

In that group, 250,000 households in the region are officially defined as “severely cost burdened” by housing. That means they spend more than half their income on rent or mortgage, and utilities. The conventional goal is to pay 30 percent or less.

In the next seven years, the number of such stretched households in the area is expected to rise by 100,000.

In addition to the pure economic hardship, high housing costs are a major headache for employers seeking to attract and keep talent.

Beth Blaufuss, president of Archbishop Carroll High School in the District, said she and other local school leaders regularly lose a significant number of quality teachers to other parts of the country because of rent and home prices.

“This coming year, I know that some of [our] phenomenal young teachers who talk about loving our school are moving to places like Pittsburgh and North Carolina, and one of the major factors in their move is the cost of living and specifically the cost of housing in D.C.,” Blaufuss said.

High housing costs also hurt the quality of life for everybody in the region by adding to traffic gridlock. When the only affordable homes are in the far outer suburbs, it means longer commutes and more cars on the roads. The problem is so acute that some people commute regularly to the area from the Shenandoah Valley or southern Pennsylvania.

In the long run, according to the housing leaders group, it’s critical to provide more affordable housing to avoid aggravating social and economic inequality in the region.

Real estate executive Joshua Bernstein, who represents the Federal City Council on the group, said economic development in recent years hasn’t been sufficiently shared.

If nothing is done about housing costs, he said, “you’re probably going to have increased segregation of the city, and more and more poor people being pushed into pockets of poverty, or out of the city.”

Bowers, of Enterprise Community Partners, said the preferred alternative is “a multi-income, multiethnic region that’s vibrant.” To get there, he added, “the political will is crucial.”