President Sadat's aim during his talks in Washington this week is to ensure maximum Egyptian input into a new US Middle East policy that the White House wants to bear the Reagan rather than the Carter brand.
When the Republican administration took over, it inherited from the Carter administration one of the latter's major diplomatic achievements: the Camp David formula for a Middle East settlement. But the Camp David process has been stalled for months on the tricky question of autonomy for Palestinians, on which the Israelis had given an undertaking in the original Camp David accords.
There were reports from US Secretary of State Alexander Haig Jr.'s party during his visit to Mexico last weekend that the Reagan administration was thinking of taking a second look at the Camp David formula. These followed speculation that Mr. Reagan would like to broaden Camp David so that he would upstage former President Carter and get his share of credit for any progress toward a Middle East settlement.
It is difficult to see how Camp David could now be completely ditched. But interestingly, as some Arab and Western sources point out, the recent persistent Middle East diplomacy of US envoy Philip C. Habib has produced possible openings for some modification or enlargement of the Camp David formula for eventual overall peace between Arabs and Israelis.
Whether this was the Reagan administration's intent from the outset of the Habib mission -- never once publicly associated with the stalled Camp David process -- is not clear. But Mr. Habib's diplomatic success, ostensibly centered on lessening a threat of wider war in Lebanon, nevertheless has had the following consequences:
* It has raised the possibility of widening the Camp David negotiations to include Lebanon, from where the Palestinians (and more particularly the Palestine Liberation Organization) have mounted their main attacks on Israel.
* It has established a precedent for a negotiated cease-fire between Israel and the Palestine Liberation Organization (PLO) -- even though the negotiation was indirectly conducted through the US and the UN. Although this step is still short of including the PLO in Middle East settlement negotiations -- which the US and Israel refuse to do but which European governments and others think a prerequisite for effective progress -- it could be a step in the right direction.
* It has given the PLO an opportunity in wake of the Lebanon cease-fire to prove its "responsibility" and the authority of its leadership -- as against the Israeli contention that it is a splintered organization of nothing but murderers and terrorists.
* It has seen the establishment of an Arab consultative group (Saudi Arabia, Kuwait, Syria, and Lebanon) which worked in tandem with Mr. Habib in the latter's negotiation of the Israel-PLO cease-fire in southern Lebanon. If the group remains active, and if Lebanon is brought into the Camp David negotiations , Arab lands other than Egypt might be on their way toward participation in the US- sponsored Middle East peace negotiations -- long an aim of US diplomacy.
* If all these pieces fitted together, Mr. Reagan would indeed be able to move forward having put his personal mark on the US Middle East peace effort.
Nothing dramatic is expected before Israeli Prime Minister Begin, Jordan's King Hussein, and Saudi Arabia's Crown Prince Fahd have in turn followed Mr. Sadat to Washington this summer for talks with President Reagan and Secretary of State Haig. One line of speculation is that after these visits, when all the pieces have been fitted together, Mr. Habib might be appointed US Middle East peace negotiator, a post last held under the Carter administration by Sol Linowitz.
There is no official confirmation from the US side that the Reagan administration is in fact working on any such fragile blueprint as outlined above. If indeed it is, Washington would still need to secure the acquiescence of Egypt and Israel, the two other participants in the negotiations hitherto.
Egypt could be expected to say "yes." The Egyptians see a greater US commitment to rebuilding the strength and authority of a reunited Lebanon as likely to lessen the influence there of: (1) Israel; (2) Israel's mercenary client force in southern Lebanon under maverick Lebanese Christian Maj. Saad Haddad; and (3) Syria. This three-pronged effect would suit the Egyptian national interest in the Middle East.
Israel, for its part, might demur. Like Egypt, Israel is keen to see the Syrian presence and influence in Lebanon reduced. But the Israelis would probably resist removal of Major Haddad's force from southern Lebanon, doubting whether either the Lebanese Army or any UN force could provide the same kind of reliable buffer as the major's mercenaries against possible PLO incursions into northern Israel.
One other caveat: Whatever widening there might be of the Camp David formula Egypt and Israel, each have a point on which they are likely to stand firm.
Egypt will resist anything likely to delay Israel's final withdrawal from all the remaining territory it still holds in Sinai, due next April.
Israel under Mr. Begin is likely to resist anything seen as blocking definitively the Israeli hard-liners' commitment to eventual extension of Israeli sovereignty over the West Bank -- or Judea and Samaria, as they call it -- in their eyes, the fulfillment of Old Testament promi se.