The Carter administration is engaged in an unusually sophisticated gambit with Congress to try to win approval for its controversial plan to sell warplanes simultaneously to Egypt, Israel and Saudi Arabia. As of now, the administration is convinced its gambit is working.

In its early months the administration tended to send controversial proposals to the House and Senate with little warning or planning, but from its beginning the planes sale has been handled more carefully. If the administration succeeds, the lesson could be an important one.

The gambit began with the idea of a "package deal." No previous president had dared to propose that the United States sell such lethal arms to potential opponents of Israel. President Carter took the dare with a new idea: Let the United States sell the weapons to Arab states in tandem with a comparable sale to Israel.

The import of the combination was not left to Congress' imagination; administration officials said that the House and Senate would have to approve the sales of 50 F-5s to Egypt and 60 F-15s to Saudi Arabia or the president would refuse to make the sale of 15 F-11s and 75 F-16s to Israel.

This notion infuriated Israel and its old friends in Washington, including the loose alliance of groups, largely Jewish organizations, known as the Israeli lobby. The prospect of advanced American warplanes in Saudi Arabia and to a lesser degree (partly because the planes would be less advanced) in Egypt, displeased them enormously.

Probably more painful for Israel and its friends was the implicit change in what they regarded as a "special relationship" between Washington and Jerusalem. Historically, when the Israelis asked for U.S. arms, the American government provided them. Suddenly, a new American president took the position than an arms sale to Israel could be compared to - indeed, be made dependent on an arms sale to Egypt and Saudi Arabia. Hardly a special relationship.

The Israeli lobby mounted a campaign to stop the sales, initially with great confidence of success. Its members thought at first they would win congressional majorities to disapprove the sale of the F15 to Saudi Arabia, while letting the sales to Egypt and Israel go through. Then, they calculated, it would be up to Carter to enforce the "package" idea and the Israeli lobby reckoned that he would find it politically too expensive to do so.

Their first tactic was to make an issue of the "package" idea. With substantial congressional support, the friends of Israel argued that Carter had abrogated a congressional prerogative by arbitrarily combining three arms sales. Pressure built in Congress to split up the package.

The administration officials who were orchestrating the package deal regard this as a blunder. "By making [TEXT OMITTED FROM SOURCE] of them said last week, "they gave us an easy one to give away."

Carter gave it away in a letter to key senators. He dropped the world package, and said he welcomed congressional consideration of each sale independently.

At the same time, Carter reserved the right to proceed as he saw fit after Congress acts - in other words, to reactivate the package, which, his aides say, he fully intends to do.

(In his most optimistic assessment yet, Byrd said Saturday that even if the Foreign Relations Committee passes a resolution disapproving the sales, the Senate isn't likely to endorse it.

"I believe there is ample support as of now in the Senate to reject any disapproval resolution," Byrd said at his weekly news conference. "There is strong support for the three elements, the three proposals."

(The administration, he said, can avoid a confrontation by providing senators three assurances: that jets sold to Saudi Arabi not be based at the city of Tabuk, where they would be in an easy position to attack Israel; that the Saudis use their jets only for defensive purposes; and the U.S. committment to sell jets to Israel will be expanded past 1984.

Nevertheless, the shift in appearances was enough to please the Senate majority leader, Robert C. Byrd (D-W.Va.), and other key congressional leaders. Almost overnight the prospects for administration success, particularly on the Senate floor, rose significantly.

By this past week the Israeli lobby had been forced to change tactics. No longer confident it could block the Saudi sale, it now favors deferring all three proposed sales. (Israel itself will not openly support this tactic, but nor will it openly denounce it). Twenty-one members of the 37-member House Committee on International Relations, which must pass on a resolution of disapproval of the sales, signed such a resolution against all three.

The House committee is now the focus of attention for the White House and the substantial pro-sale lobby that has come together. That group consists of hired agents of Saudi Arabia, various pro-Arab groups, the manufacturers of the planes, the international oil industry and other sympathetic business interests.

The sale's backers reckon that if they can persuade just three of the House members who signed that resolution of disapproval to change their minds, the House committee will reject the resolution and the three sales can go through.

And the administration has saved a trump card designed to win over those three votes. That is a promise to sell Israel more planes than the package contains a sweeter pill.

This afternoon Deputy Secretary of State Warren M. Christopher, from the outset an important architect of the administration's strategy, will meet with members of the House committee to offer the compromise. It will not be large, administration sources promise, but they hope it wil be sufficient.

If it fails, the issue will probably reach the floors of both House and Senate.

The White House says it wants to avoid a showdown floor vote, to spare the Israeli lobby the embarrassment of its first major defeat in history. "Their fall could be a dramatic one," an administration official said, "way out of proportion to this sale issue."