Scores of social service agencies will urge the D.C. City Council today to reject Mayor Marion Barry's proposed budget cutbacks, and one of the mayor's staunchest allies on the council is calling on him to come up with alternatives to cutting programs for the needy.

Council member Polly Shackleton, chairman of the committee on Human Services and one of Barry's most loyal supporters, has told the mayor's budget aides she expects them to come up with alternatives by next week to the mayor's plan to eliminate the General Public Assistance program in fiscal 1984.

The $14 million General Public Assistance program provides aid to about 5,500 temporarily disabled and unemployed persons, most of whom would receive less assistance or no aid at all if the program is abolished.

Shackleton is to begin two days of council hearings on the city's huge Department of Human Services today at the District Building. More than 60 nonprofit social service agencies--three times the number last year--have signed up to testify against the cuts. Aides to Shackleton said many others who asked to be witnesses were told they could submit written testimony only.

The Washington Council of Agencies, an umbrella group that represents 165 private, nonprofit organizations, has estimated that the city's contracts with local charitable groups would be cut in half under the mayor's proposals. Barry's budget aides, who will lead off the testimony today, dispute the group's estimates.

Barry and department heads have been holding nightly meetings with representatives of community groups to try to defuse some of the criticism of his budget.