"They're eyeall to eyepatch, and you can't tell who linked" was a gag that went the bunds here the other night when President Carter met with Israel Foreign Minister Moshe Dayan. It turned up to be a prescient line.

Not only does the major upshot of their meeting - the prospects for a meaningful Geneva Peace Conference remain doubtful. But the fact of the encounter itself demonstrated the keeper truth that the Carter administration is pursuing a no-win diplomacy in the Mideast.

The centerpiece of the administration's approach is the drive to get a comprehensive implies all issues, not just those type for settlement, and all parties, not [WORD ILLEGIBLE] moderate ones. So all along the Carter administration has been bouncing back and forth between extreme lements on issues that cannot now be resolved.

At the outset Carter moved beyond the moderate elements on the Arab [WORD ILLEGIBLE] - the government of Egypt and Jordan - which were prepared to move toward recognition of Israel in exchange for pieces of territory. He tried to bring in the Palestine Liberation Organization as well as the Syrians, who consider themselves the point-men of Arab Nationalism. To do this he came out for a homeland for the Palestinians.

The American commitment to a homeland for the Palestinians came fast as the most moderate group of Israelis - the Labor Party, including such Veterans of negotiations with Washington as Prime Minister Yitzhak Rabin and former Prime Minister Golda Meir - was falling apart. Elections in May brought to power a new group led by Prime Minister Menahem Begin, which was disposed to see all Arabs as terrorists and all Americans as appeasers.

To reassure Begin, the President gave him an extremely warm welcome when he visited Washington early in the summer. That brought Begin the solid support of the American Jewish Community.

Since Begin denounced the PLO and refused to negotiate with them. Washington had to find some covert means of bringing the Palestinians to Geneva secretary of State Cyrus Vance developed the notion that the PLO should first assert its good faith by accepting Security Council Resolution 242, which implicitly recognized Israel. he was then prepared to have the Plo admitted to Geneva as part of an all-Arab delegation including representatives from Egypt, Jordan and Syria.

Begin balked again, and the PLO - with nothing to gain - refused to accept Resolution 242. Under those circumstances, the United States worked up with its co-chairman of the Geneva conference, Russia, a joint statement calling for an early resumption of the talks.

The joint American-Soviet declaration was a last-ditch effort to bring the PLO and the Syrians to Geneva. It included pleasing references to the "legitimate rights of the Palestinians" and avoided thorny issues such as Resolution 242.

It might have worked. Except the Israelis and their supporters in this country sensed in the language the elements of a betrayal. With a storm building up against the Carter administration in Congress, the President and Dayan got together in New York Tuesday night.

Their joint statement reasserted U.S. commitments to Israel and pleased both the Begin government and the American Jewish community. But by the same token it worried the Syrians and the PLO. Though they have been holding fire, it is not at all clear that they will go to Geneva - at least not in a way that can yield productive negotiations with Israel.

The moral of all this is that there is no way to satisfy simultaneously all the different parties and interests in the Mideast. President Carter cannot both woo Palestinians and have the friendship of Israel; nor apply pressure on Israel and be loved by the American Jews.

"I would rather commit suicide politically than hurt Israel," he told a group of congressmen at the White House on Thursday. That is a noble sentiment of support.

But a President of the United States shouldn't have to make it. Carter was obliged to because he is trying to do too much at once in the Mideast. So the immediate priority, whether there is or is not a Geneva Conference, is to sort out the issues and the parties and begin making the modest progress that is possible, instead of chasing after the total settlement that is clearly not possible.