WASHINGTON  The fight over a proposed same-sex marriage law here heated up this week as the Roman Catholic Archdiocese of Washington said that if the law passed, the church would cut its social service programs that help residents with adoption, homelessness and health care.

Under the bill, which has the mayor’s support and is expected to pass next month, religious organizations would not be required to perform same-sex weddings or make space available for them.

But officials from the archdiocese said they feared the law might require them to extend employee benefits to same-sex married couples. As a result, they said, the archdiocese would have to abandon its contracts with the city if the law passed.

The church’s social services arm, known as Catholic Charities, serves 68,000 local residents, including about a third of the city’s homeless people, who go to city-owned shelters managed by the church, city officials said.