The D.C. City Council yesterday restored $10 million to next year's proposed budget for the public schools afer Mayor Marion Barry dropped his once-vehement opposition to the move. But school officials said they still face shortages in the current year that may require teachers to be furloughed or laid off.

The vote defused an angry squabble between Barry and the school board that boiled over in public charges of duplicity and bad faith, but it did not settle the question of how much money the schools will actually have to spend next year.

Council Member John A. Wilson (D-Ward 2), chairman of the committee on finance and revenue, renewed his challenge to the credibility of Barry's entire financial program, saying that "it makes no sense to give money to the schools when you know it doesn't exist," and predicted that Congress would take away the funds that the council agreed to give.

Transferring the $10 million out of funds earmarked by the mayor for debt service, or the payment of principal and interest on long-term loans, the council set the school board's spending level for the 1982 fiscal year at $248.2 million.

Barry had proposed $238.2 million, which would have been less than the schools are receiving this year; the school board asked for $265 million, and cooperated with citizens and parent's groups that launched a campaign to pressure the council into "full funding" of their request.

Barry argued that the school board did not submit enough information about how it spends the money allocated to it to justify the kind of increase the board was seeking. His view drew support yesterday from the U.S. Senate as it belatedly approved the city's budget for this year and adopted language saying the public schools' budget request was "totally void of worthwhile information."

A week ago, Barry objected strongly to the plan devised by Council Member Betty Ann Kane (D-At-Large) to transfer the $10 million. He called it "ridiculous" and said she was "playing silly games" with the city's future.

But after meeting with Kane, other council members, school officials and angry parents, he accepted it. "I made some adjustments in my attitude," he said.

The transfer of the $10 million out of the debt service account does not mean the city will fail to make any loan repayments that are actually due. It means that some borrowing this year and next year have to be deferred, and that a proposal by the city's accountants to advance the repayment of existing loans will have to be modified. Barry said the principle of that proposal "has been preserved," and that's what I was fighting for."

School Board President R. Calvin Lockridge, a vehement critic of Barry, said the council's action was "no favor to us, but we'll take it."

The schools' immediate problem, he asid, is not what will happen next year but how to get through the current year. The most money that Congress will probably authorize the schools to spend, he said, is $246 million, but current rates of spending would result in outlays at least $8 million greater. The only way to cut that deficit, he said, is to lay off another 300 to 400 staff members or to furlough the entire school system for 10 to 12 days.

Vincent E. Reed, the superintendent of schools, confirmed that he has proposed to furlough all employes for 10 days. Those days, he said, would be days when the staff usually works but classes are not in session, so no children would lose instruction time. The board has not yet acted on his proposal and Lockridge said it would not do so until congressional action on the budget is complete.

While the minidrama of the $10 million was unfolding, however, Wilson, who has emerged as the Cassandra of the council in the battle of the budget, renewed his attack on the entire process.

Wilson has been saying that the revenue estimates that are the basis of both this year's budget and next are unrealistic, and that multimillion dollar additions to the cumlative city deficit are inevitable.