There are plenty of reasons why the District of Columbia's special program to channel millions of dollars into minority contracts is not working, a City Council inquiry was told this week.

Witnesses said the reasons range from politics and a sluggish administration to budgetary problems that leave the D.C. Minority Business Opportunity Commission with a woefully inadequate staff.

Milton G. Carey, former vice chairman of the minority commission, who resigned last month, said: "It is not the law that has not worked; it is the people (in Mayor Walter E. Washington's administration) who have not worked."

Carey said the program has channeled only $2 million, far less than the potential, to minority firms.

However, Joseph P. Yeldell, general assistant to the mayor and a main target of Carey's wrath, said in effect that the program is trying to bite off too much in a hurry.

Yeldell placed some of th e blame on the council, saying tha minority business panel was "one of seven commissions established by the council without any (budgetary) resources to operate on . . . It is one thing to pass a law and something else to implement it."

But Carey repeated his earlier estimate that he program could have channeled as much as $85 million into contracts for minority firms. Teldell caleed that figrure "mythical," saying the true total would have been a fraction of Carey's estimate, partly because Congress has not approved a formal 1978 budget for the city.

The hearing, a notably placid one, considering the emotional charges and counter charges, was conducted by Wilhelmina Rolark (D-Ward 8), who heads the council, not just members of the committee, attended at least part of Monday's all-afternoon session.

Once again, the session posed - but did not answer - the ultimate question: Given a long history of economic and social discrimination, are minority-owned firms capable now of providing the millions of dollars of goods and services that the program is designed to channel tham?

Briefly, here is the background of the issue:

Early last year, the council passed a bill requiring that 25 percent of all contracts awarded by the city each year should go the minority-owned firms. The oversee the program and cetify firms, the bill established the seven-member Minority Business Opportunity Commission.

Initially, six members were chosen, and thay split 30 to 0 between chosing Grey or James L. Dension as chairman. When a seventh member, builder William T. Syphax, was chosen four months later, he broke the deadlock, choosing Dension. Carey became vice chairman.

Dension resigned recently to become a member o fD.C. Board of Electronis and Ethics. Carey, who is president of the Metropolian Contractors Association, made and yeldell.

Carey's eight-pager statement, which he read at Monday's inquiry, centered on the mayor's failure to appoint a staff director for the commission within 60 days, as required by law, and with what he described as sluggish administration under Yeldell, who - over Carey's protest is filling in as the director.

Yeldell insisted that budgetary problems have prevented the oppointment of a permanent director and other key personnel. He said Melvin Washington of the Corporation Counsel's office is now in line for the director's post.

Council Chairman Sterling Tucker looked to the future, asking Commission Member Syhax: "Is the law workable?"

We've been going through a lot of growing pains," Syphax replied, "but the law is workable."

Tucker, who is an announced candidate for mayor, observed: "It would be a shame if the D.C. government did not make this law work . . . I am not convinced the government is serious yet about implementing this law. . . I think that is very sad."

Yeldell disagreed. Although Mayor Washington vetoed the first version of the bill in 1976, "We are committed to the bill, "Yeldell, said. "I don't think we're going to settle anything in an adversary role.

Partly defending the administration and partly acknowledging shortcomings, Yeldell sid the council-passed law failed to deal the counci1-passd law failed to deal realistically with legal requirements for bonding of contractors.

Yeldell also contended that few minority owned firms are large enough or financially strong enough to handle multimillion-dollar contracts given the city.