Although President Carter has been unable to ingratiate himself with American business despite high-volume promises of a 1980 balanced budget, his relations with George Meany and the AFL-CIO have dropped to the lowest level of any Democratic President since Harry Truman a quarter of a century ago.

Inside the AFL-CIO's 16th St. palace overlooking the White House, Meany himself recently delivered the ultimate rebuke in the privacy of his office - that Jimmy Carter "may be the most conservative President since Herbert Hoover."

That such a description seems a gross exaggeration misses the point. The point is that almost five months into its first term, the Carter administration has gained the unusual reputation of being no friend of business and no friend of labor, an alien in both camps and a comfort to neither.

Indeed, the political connection between the Carter White House and the top ranks of the AFL-CIO was quietly - and totally - severed several weeks ago, not by some lieutenant but by Meany himself. The estrangement followed the first of what was to be a series of informal lunches. That luncheon, hosted by Hamilton Jordan, Carter's chief political aide, was held in the White House mess.

Present, among others, were the new chairman of the Democratic National Committee, former Maine Gov. Kenneth Curtis (picked by Carter for the uneviable job of carrying out political orders from the White House) and the AFL-CIO's top political operative, Alexander Barkan.

The date was March 31, the very day that the Democratic National Committee snubbed Meany and the AFL-CIO in the election of new members to the executive committee. Meany himself was not all that provoked by the snub and about a week later Barkan, hoping to follow up Jordan White House hospitality, invited Jordan and his deputy, Landon Butler, to a lunch at the Hay-Adams, also with Curtis present.

"It was a home-and-home affair," an AFL-CIO official told us. But before the second lunch could be held, Meany ordered it called off.

That anti-Carter decision by Meany, in contrast to the Truman record, came not as a result of any particular Carter administration perfidy. The brief hostility between Truman and big labor was brought about by the President's attempt to break a railroad strike by drafting workers. Generally, relations were healthy between Truman and the labor unions that supplied the margin of muscle that elected him in 1948.

With Carter, no single act suddenly brought Meany to a boil. Instead, a series of administration gaffes and ingratitudes, following labor's contribution to Carter's narrow victory, has systematically shattered confidence.

Although on the political side Meany's men complain that Democratic National Committee rules have restricted labor membership to a mere 15 in favor of women and minorities, the real grievance is legislative. Meany's serious purpose is to compel the Carter administration to be far more cooperative on what the labor unions see as their life blood in new legislation from a Democratic administration.

Thus, Meany's order to break all top-level political contact with the Carter White House stems directly from legislative failures, the most painful of which was defeat of the situs picketing bill - long a labor "must."

At that first - and last - White House luncheon, a Meany agent complained to Jordan about Bert Lance, Carter's budget director and most powerful economic adviser. Meany was angry, Jordan was told, because he had irrefutable evidence that Lance had quietly lobbied against the situs picketing bill, despite Carter's pledge of neutrality. Jordan did not deny the charge, but replied, "Tell your people it is still early in the game."

That was over two months ago, and nothing he has seen since then has changed Meany's opinion that the man in the White House is no friend of labor. Indeed, AFL-CIO operatives have all but given up on Carter's help for the next major labor issue - the minimum-wage bill - and they blame the frosty congressional reception for universal voters registration on administration stupidity.

No Democratic President in modern times has engaged in so many running disputes with big labor - and with so little profit from business to show for it.