President Carter's failure to win Saudi Arabia's consent to delay the promised U.S. sale of 60 F-15 aircraft confronts him with his clearest test posed by this question: Can the United States have its own Mideast policy, or only one tied to Israel?

The answer to that question may well decide the future of the vital U.S.-Saudi connection. At issue is whether Saudi Arabia will continue to underwrite U.S. domestic oil needs over the bitter opposition of Venesuela, Iran and other oil-rich members of the Organization of Petroleum Exporting Countries (OPEC) lobbying for higher prices. Changes in Saudi oil production and pricing, more over, could wedge Western Europe and Japan away from the United States, undermining political unity of the industrialized democracies.

As provided by Sen. Frank Church (D-Idaho), soon-to-be chairman of the Senate Foreign Relations Committee, the answer to this crucial question is a clear "no." Indeed, Church's letter to Secretary of State Cyrus Vance - signed by at least nine other senators - protesting the sale was couched with generous overstatement in terms of how Israel views the sale, but not in terms of U.S. interests.

"Church wrote his letter like a senator from Israel," one of Church's colleagues (by no stretch of imagination anti-Israel) told us. Church's letter was so devoid of sensitivity for the U.S. interest that Sen. Jacob Javits (R-N.Y.), long one of Israel's chief congressional defenders, did not sign it. Instead, Javits wrote a letter of his own to Vance, along with Minority Leader Howard Baker (R-Tenn.) and two other senators. They asked for a delay in the sale until a committee study is finished. That study is expected to go beyond Saudi Arabia to the implications of U.S. arms sales throughout the Middle East. Sen. Araham Ribicoff (D-Conn.), a lifelong leader of the American Jewish community who cannot be faulted on friendship for Israel, signed neither letter, but privately informed one senator that he agreed with the Javits, not the Church, approach.

In a clumsy attempt to finesse the political dilemma of whether to deliver on his pledge to sell Saudi Arabia the planes, or to surrender to Church and Israel, Carter so far has struck out.

During his stop in Riyadh a month ago, Carter renewed his pledge - then, after reading Church's Jan. 23 letterM had second thoughts. He ordered Ambassador John West to seek Saudi agreement to delay the sale (which can be blocked by Congress during a 30-day period following its submission to Capitol Hill).

The predictable failure of West's mission three the White House and the National Security Council into a tail spin. A new NSC study was ordered, which meant postponing submission of the F-15 deal, with or without Saudi agreement, beyond the Feb. 1 date originally planned.

These delays are feeding pro-Israeli propaganda, which is now warning about an Israeli "pre-emptive" air attack on Saudi F-15 bases if war again threatens between Israel and the Arabs.

That warning is that warning is contained in a 10-page attack on the sale by the American Israel Public Affairs Committee (AIPAC), brilliantly reasoned from Israel's vantage point. AIPAC concedes that Israel itself is now acquiring 25 F-15s from the United States and has asked for 25 more, but claims Israel's need "is more acute than that of Saudi Arabia."

Yet, last March, before becoming foreign minister, Moshe Dayan was quoted as publicly stating that Israel has "more planes than Italy or Germany or France and a little less than England."

The political reaction in Saudi Arabia to Jimmy Carter's equivocation in the face of Israel's displeasure was predictable. It began with a private letter to Carter by the Saudi ambassador politely asking that the pledge (first made by the Ford administration) be carried out.

But the Saudi government would not be human if, in the face of a dishonored pledge, it continued to resist oil price hikes demanded by other OPEC countries or if it continued high-rate oil production just to satisfy Carter.

Worse, the Saudi could succumb to OPEC pressure to sell crude oil in a "basket of curriences," costing the dollar its pre-eminent currency position. That would mean a price break for strong currencies (the West German mark and the Japanese yen). Such a damaging policy switch for Western unity will be pressed at the next OPEC meeting in June.

But underlying these surface hazards is the spectacle of the U.S. superpower once again squirming in public over an arms sale in the Middle East clearly tailored to it own interests. This spectacle reflects an increasingly dim image of the United States - not only to Saudi Arabia but around the whole world.