A majority of D.C. Council members indicated yesterday that they would support scaling back the city's law guaranteeing overnight shelter for the homeless when the issue comes up for a vote next week.

Meeting as the Committee of the Whole, the council members agreed to schedule a vote on a measure to reduce emergency shelter benefits to the homeless now provided under Initiative 17.

Proponents of the measure, including council member H.R. Crawford (D-Ward 7), predicted that the council would vote overwhelmingly in favor of it as a means of saving the District millions of dollars annually.

The current law, approved in a 1984 voter initiative, mandates that the city spend whatever it takes to provide shelter for homeless people who request it.

Under the plan sent to the full council for a vote next Tuesday, the city would set a limit on how much it would spend each year to provide shelter for the homeless. If the shelter budget is exhausted, the mayor could shift funds to it from other projects.

The proposal has drawn criticism from advocates for the poor, who contend that some homeless people will be turned away if funds run out.

However, Crawford and other proponents say the cost of sheltering the homeless has gotten out of hand.

The cost of implementing the law has nearly tripled, from $10 million in fiscal 1985 to $27 million in fiscal 1988. Local judges have issued rulings forcing the city to provide trailers and take other costly measures to comply with the law.

The proposed change in the law also would require homeless people who have jobs or receive public assistance to pay up to 30 percent of their income to the city for housing. Others with no income would be required to provide community services.

Crawford, saying that many shelter residents have the means to pay, told the committee that some homeless people get veterans and other government benefits and maintain savings accounts and safe-deposit boxes. The Human Services Committee, headed by Crawford, approved the plan last month.

Crawford's plan would impose a 30-day limit for single people living in shelters and a 90-day limit for families.

"We've had some people stay in shelters for up to two years," Crawford said.

Also under the plan, the mayor would appoint a shelter program coordinator to screen shelter applicants and steer them to mental health and drug counseling services if needed and also try to help them find affordable housing.

Council Chairman David A. Clarke (D) voiced concern about the eviction provisions of the proposal and their potential impact on children.

As proposed, families with children could be evicted if the parents violate shelter rules or if their 90-day limit expires.

Crawford, in a heated exchange with Clarke, said that depending on the circumstances, children could be sent to foster care or the mayor could extend a family's shelter stay.

Clarke also questioned whether fund cuts would affect homeless people more than shelter providers. Clarke in the past has said some shelter providers receive a disproportionate share of shelter funds in contracts.