Many of the worst shortages are in major cities with healthy local economies, like Seattle, San Francisco, New York and Washington. “We’ve seen a huge loss of affordable housing stock,” said Jenny Reed, the policy director at the D.C. Fiscal Policy Institute. “We have lost 50 percent of our low-cost units over the past 10 years, and at the same time, the number of high-cost apartments, the ones going for more than $1,500 a month, more than tripled.”

The squeeze comes both from supply and demand. Even as the housing market has started to turn around, the number of renting households has continued to climb — by a million in 2011 alone, the biggest annual increase in three decades. Many Americans have lost their mortgaged homes and chosen to rent. Others were unable to obtain financing for a purchase, because of a loss of income or tighter credit standards.

In many markets, investors have rushed to meet the new demand by building new multifamily housing units or by buying up foreclosed homes and renting them out. But that has not translated into a surge of new units available to low-income renters.

“Builders always are aiming at that higher end,” said Jed Kolko, the chief economist at Trulia. “And eventually, as those new units age, they trickle down to lower-income borrowers.”

But not now. With demand surging, inventories are shrinking, vacancy rates are falling and rents are rising at the low end.

The long-term federal budget cuts known as sequestration are only adding to the problem, hitting housing programs especially hard. Many local housing authorities, which rely on federal funds, have stopped rolling over vouchers, leaving even more families on waiting lists, to fend for themselves in rental markets where prices keep rising.

“I can’t emphasize enough how draconian these cuts have been on the backs of the poorest folks in the country,” said Sunia Zaterman of the Council of Large Public Housing Authorities.