In New York City, which has been counting its homeless population since 1982, the number of families without shelter rose to an all-time high of 9,500 in October. Parents and children now make up 80 percent of the city’s homeless because the number of single adults without homes in New York has dropped by 19 percent over the past three years.

A study by the Pratt Center for Community Development offered one explanation for the trend: In city neighborhoods, where most of these families come from, the number of households paying more than half their income for rent shot up 30 percent in just three years, between 2002 and 2005.

Although rents are far outpacing wage increases for even the middle class nationwide, the very poor are feeling the most pain, advocates and academics say. The crunch in available and affordable rental housing, they say, is manifest at the bottom of the income scale by an increase in homelessness.

“The housing market is like a game of musical chairs,” said Steven R. Berg, vice president for programs and policy at the National Alliance to End Homelessness. “When the music stops, somebody’s going to be left without anything.”

The squeeze is also fueling a disagreement among advocates for the homeless over the best direction for federal policy. The debate is going on now in Congress, where competing views on how to reauthorize federal support for homeless families are making their way through the House and Senate.

The McKinney-Vento homeless assistance programs, which were created in 1987, are among the few programs within the Department of Housing and Urban Affairs to receive a budget increase in recent years. Money for homeless assistance has risen by $213 million since fiscal 2005, to $1.4 billion in 2007.

But some groups say that increase has been targeted largely at single adults with substance-abuse problems or mental illnesses. They are pressing for a change that would allow more families to receive aid. Meanwhile, organizations serving the “chronically homeless” population of single adults say the federal program isn’t big enough to support a huge influx of new beneficiaries, which they say could be as large as 10 million people.

The central question is how best to help the homeless families who are hardest to count — those without permanent shelter, who may be paying rent week-to-week in hotels or living doubled up with relatives. Those families count as homeless when they seek services financed by the Department of Education, but they don’t qualify for services for the homeless financed by HUD.

Groups such as the National Policy and Advocacy Council on Homelessness say HUD should include doubled-up families, and they support a House measure that would be more inclusive. The House Financial Services Committee has scheduled a hearing for this week on the reauthorization of McKinney-Vento.

“We don’t think anybody in this country should be homeless, and certainly not living on the street,” said Jeremy Rosen, director of the NPACH. “Nevertheless, chronic homelessness has certainly had a very negative and detrimental impact on resources and policies available for ending homelessness for children, youth and families.”

Advocates on that side of the issue point to statistics such as the New York figures that show a drop in homeless adults as a sign that the aid is skewed toward one group.

Gloria Guard, president of the People’s Emergency Center, a Philadelphia shelter that serves families, said her organization has had to cut back on its workforce training programs and other supportive services as federal aid has shifted toward permanent housing for the chronically homeless. When residents leave the shelter, she said, they have few options. “The only housing for the families that we see, whose mothers are neither mentally ill nor addicted to drugs, are the projects,” she said.

Advocates on the other side of the issue are more supportive of a Senate bill that wouldn’t broaden the program’s scope. Berg said his organization believes that the McKinney-Vento funds should focus on the relatively smaller population of about 200,000 adults who chronically sleep on the streets. The issues faced by doubled-up families, he said, would be better addressed by increases in spending for other HUD programs that are directed toward producing affordable housing and subsidizing rents.

“Everybody has every reason to be very upset at the fact that there’s so many people who don’t have decent housing,” Berg said. “They should be upset at the disinvestment in federal housing programs that has occurred over the past five years.”