THE TANGIEST part of Anwar Sadat's mission in Washington was to advance his proposal that the United States open up a direct line to the Palestine Liberation Organization. Well, he made the proposal. The Reagan administration said no, apparently on two grounds: 1) that it has only begun to put together a policy and wants to go slowly and consult others, and 2) that the United States promised Israel in 1975 not to recognize or negotiate with the PLO until the PLO accepts Israel. But that is not the end of the matter.

The administration, in saying it wants consult on the one hand and keep its commitments on the other, is hardly making a definitive response. The relevant question is whether, after completing consultations the administration will and should keep its commitment to shun the PLO if Israel does not keep its Camp David commitment to open a reasonable negotiating door to the Palestinians. So far, the Begin government has barred the door: this is the practical meaning of its policy of expanding Jewish settlement in the West Bank and offering a form of Palestinian autonomy without dignified content.

Will Mr. Begin, when he arrives in Washington after Labor Day, be ready with proposals to move the autonomy talks off ground zero? That might let the PLO issue be sidestepped for a while. Otherwise, it seems to us, the administration will be unable to avoid asking whether the best way to bring the PLO to recognition of Israel, which should be the whole point of the exercise for the United States, is by going straight to the PLO. Mr. Begin repudiates the notion of PLO recognition, since he insists that the PLO is a terrorist group with no valid claim of its own to statehood. We are in that very large company, however, believing that to "the Palestinian question," as to "the Jewish question" before it, there is not other acceptable answer. The problem is not the destination but the path.

The impression should not be left that only Israeli "inflexibility," in a much used word, stands between the Middle East and peace. Palestinian intransigence is deep, and matching it was freshened the other day by a top PLO official, Farouk Khaddoumi. He declared in the German weekly Stern that the PLO will never accept Israel's right to exist and that even pre-1967 Israel must be destroyed. Mr. Begin promptly cited the interview.

Just as there can be no doubt about the authenticity of Mr. Begin's expressions, there can be no doubt that Mr. Khaddomi's words represent a strong current in PLO policy and in Palestinian hearts. And each of them seeks to take refuge from difficult political decisions behind the other's words. The American task is, with others, to see if they will make those decisions.