Except for a scattering of construction unions, organized labor feels strongly that Raymond J. Donovan should resign from his Cabinet office of secretary of labor.
President Reagan's continuing support of the former construction company executive has become another strain on relations between unions and the administration. The labor secretary labor, on whom the White House should be able to depend to maintain sound relations with labor, has become a liability.
In an election year, many Republicans who would like union support are feeling the political repercussions of having a secretary who is generally repudiated by labor. Even in New Jersey, Mr. Donovan's home state, a Republican candidate for a House seat said recently he ''would not think of asking Ray Donovan for support.''
The primary opposition to Secretary Donovan in labor circles is not based on ethical considerations or moral judgments. Rather, labor leaders view the Cabinet officer as an ineffective advocate of workers' interests, who holds what many say is an unsympathetic attitude toward organized labor.
Union officials, except for those in construction, have almost no direct communication with Mr. Donovan. Traditionally, the secretary has been invited to labor conventions and the AFL-CIO's quarterly executive council meetings, but Mr. Donovan receives few invitations -- none from the AFL-CIO.
Because of his construction background and his experience at bargaining tables with building trades unions, Mr. Donovan has cordial -- but not warm -- relations with some leaders of the AFL-CIO's Building and Construction Trades Department. They consider him sympathetic on a number of legislative issues important to the building trades. As one official put it, ''He's the only secretary we have.''
The AFL-CIO and major independent unions were angry in 1981 when Ronald Reagan, unlike most predecessors, did not ask labor for recommendations or discuss with them Mr. Donovan's appointment before it was announced. The new secretary was unknown to labor leaders except those few who had dealt with him in New Jersey. Lane Kirkland and Thomas R. Donahue, the AFL-CIO's top officers, had never heard of him.
Although those who had dealt with Raymond Donovan said he had a record in New Jersey as a ''tough but fair'' employer, relations between Mr. Donovan and labor leaders started out badly and never improved. He is now largely ignored.
Labor interprets the Cabinet position to be one that advocates the interest of workers -- and therefore their unions -- in government. They expect the secretary to argue for them in Cabinet meetings and to support them on some issues before Congress. Mr. Kirkland and others say they are ''disappointed'' that Mr. Donovan does not do these things. Unions regard him as ''pro-business.''
Now Mr. Donovan is being investigated for alleged misconduct stemming from his relations with union officials and alleged links with mob figures back when he was a New Jersey construction executive. Secretary Donovan refuses to comment on the allegations while they are under investigation by a Senate committee and a federal grand jury.
Even if he were not being investigated, the administration would still be under pressure from labor to change secretaries. But so far, the President shows no signs of giving up on a man who was a stalwart political supporter and fund-raiser for Mr. Reagan in 1980.