Cuts in federal housing budgets over the last seven years are the major cause of homelessness among a growing number of working families and families with children, big city mayors and homeless families have told a House task force.

The budget of the Department of Housing and Urban Development has been cut by nearly 70 percent over the last seven years, resulting in a sharp drop in construction of housing that low- and moderate-income families can afford, witnesses said at task force hearings last week. Rising costs and conversion of low-cost apartments and homes to higher-cost housing also have contributed to the decrease in moderately priced housing, they said.

Spending on housing assistance has dropped from $30 billion in the last year of the Carter administration to $7 billion last year, according to New York Mayor Edward I. Koch. "The federal government has gone out of the housing business," with the only new units going to the elderly, he said.

Shanise Reese, a once-homeless 16-year-old honors student from New York, said a widespread belief that all people without homes are derelicts and mentally ill is untrue. Koch agreed, saying the "majority of people in shelters are not suffering from pathology. They're suffering from homelessness."

Reese said, "There are kids on the street hustling to survive," but homeless families "are not derelicts. We are not drug addicts. This is our country and we want to do for ourselves."

She said going to school has been difficult because of the pressure she has been under. She and her younger brothers and sisters "were humiliated by the conditions we had to live in ... . I couldn't ask people to see me at my home. I didn't have one. I had no secure place to sleep, much less to study," she said.

Her mother, Shirley Reese, who has seven other children, said, "It's very distressing that I can't provide the basic need of decent housing for my children." The family was homeless before moving into the apartment where they now live, but will be evicted at the end of the month. They have not been able to find another place they can afford.

Reese said that she could afford to pay from $400 to $425 a month in rent, but that apartments in this price range that would be large enough for her family "are not out there."

District of Columbia resident Elanor Ann Covington said she is on the waiting list for city public housing but has been told there is a five-year wait. Covington, a six-year Army veteran who left the service because of a back injury, said she was living with a friend but when the rent went up, she could no longer afford her share. Covington works at the House of Ruth, a shelter for women in the District.

A Fredericksburg couple is homeless because they earn too much money to qualify for government housing assistance but not enough to afford a place to live. Douglas Brown said he and his wife earn the minimum wage of $3.35 per hour on their jobs.

Low-cost housing is dwindling in Fredericksburg, Brown said, in part because "people are buying property in poor areas and rebuilding it so poor people can't get back in."

New York City spends about $325 million a year caring for its estimated 29,000 homeless people, whose numbers are growing, Koch said. The money comes from the city, state and federal governments, but the federal aid is not enough, he said, adding, "We can't do what the federal government is supposed to do."

Boston Mayor Raymond L. Flynn said that although Boston has a low unemployment rate, the demand for emergency housing aid grew by 21 percent from 1986 to 1987. "We have people walking from shelters to their jobs," he said.

Families with children are the fastest growing group of homeless people in the city, Flynn said.

In the past, HUD Secretary Samuel R. Pierce Jr. and other department officials have insisted there is no shortage of housing in most areas of the country. They advocate wider use of rental assistance vouchers to help low- and moderate-income families afford the available units. Vouchers cover the difference between the rent and 30 percent of the holder's income, and permit people to find their own housing on the private rental market.

In cities, however, there is a shortage of housing at any price, several witnesses said at the hearings. Asked by Rep. Barney Frank (D.-Mass.) whether she could use a voucher in New York, Shirley Reese said, "If there's no housing out there, what good is a piece of paper?"

Homeless families in many areas use vouchers and Section 8 rental assistance certificates, according to James W. Stimpson, HUD deputy assistant secretary for policy development. He said the Massachusetts State Housing Agency is using the 529 vouchers HUD allots it to find permanent housing for homeless families now living in shelters.

In addition to assistance provided under the McKinney Homeless Assistance Act, passed last spring, HUD has urged local governments to use money from older federal programs, such as Community Development Block Grants, to shelter the homeless, Stimpson said.