President Carter, Menachem Begin and Anwar Sadat are improving the chances for survival of the Camp David peace agreements they signed 10 days ago with a coordinated hardsell campaign aimed at clearing obstacles out of the way of the Egyptian-Israeli peace treaty they are rushing to establish.

While Carter and Begin appear to have become involved in a serious dispute over a Begin pledge on freezing Israeli settlements on the West bank, the Camp David Three have handled the deeper strategy of the selling of Peace with a Tinkers-to-Evers-to-Chance fluidity.

"The key to Camp David working is that the three men are politicians who understand each others' political needs and constituencies," said a high-ranking U.S. official. "If it is working well, nobody but the three of them will know how much of this phase is by design or on an ad hoc basis."

Facing vociferous heckling in the vital Knesset (parliament) debate on the accords in Jerusalem Monday from critics who accused him of opening the way to a U.S.-inspired Palestinian state on the West Bank. Begin effortlessly retrieved a strong denunciation-by-association of the Palestine Liberation Organization (PLO) delivered by Carter Saturday, and tossed it down at his critics.

Speaking to the people of Aliquippa, Pa., Carter had likened the PLO to the Nazis, a comparison that is a Begin rhetorical trademark. After Camp David, "We heard from the president of the United States from correct comparison," the prime minister proudly said.

Begin's performance in the debate and recent statements by Sadat indicate that some of the 10 letters the leaders agreed to exchange on a variety of controversial subjets after the signing of the two framework agreements were designed to be used to help sell acceptance of the overall deal sponsored by Carter.

"The letters would not exist except for their usefulness in resolving the political problems each faces," said a diplomat closely associated with the negotiations.

Begin sees his primary selling job as neutralizing criticism of him from the far right for accepting any change on the West Bank territory of the Jordan River.

Israeli officials emphasize Begin's personal dilemma in this, since most of those who have been heckling him have been his closest political associates in Begin's 30-year wait for power.

In his speech, Begin pulled out a "definitional" letter signed by Carter, which U.S. officials had portrayed as nothing more than a technical document, but which Begin cast into a strong political statement.

The letter read by Begin notes Carter's understanding that Begin interprets every mention "Palestinians or the Palestian people" as meaning "the Arabs of Eretz Israel," and every mention of the West Bank as meaning "Judea and Samaria," the biblical names of the territory.

"Everyone uses his own language, and our language is Eretz Israel and Judea and Samaria," Begin said. "This is what we agreed on and this is how it will be in the future." Eretz Israel is normally understood to mean biblical Israel, or the entire mandated region of Palestine.

At about the same time, Egyptian newspapers were headlining Sadat's interpretation of a letter from Carter obliquely restating longstanding U.S. opposition to Israel's formal annexation of East Jerusalem. The Egyptian media portrayed the Carter letter as a new U.S. commitment to get East Jerusalem back for the Arabs as a result of the negotiations Sadat has accepted.

Egyptian statements have also hinted to that country's desperately poor populace of 40 million that a successful conclusion of Egyptian-Israeli peace treaty could bring a cornucopia of American aid and investment. The Egyptian media reported statements by Sadat in Washington that the United States would now provided Egypt with a modern telephone and communications system. U.S. officials confirm that this project is under consideration, but say that it predated the Camp David results.

Even the one open dispute that has flared up over the West Bank settlements issue seems to have give Begin some political mileage. Going into the crucial vote today on dismantling Israeli settlements in Sinai, Begin has been reminding the Knesset that he is standing up against pressure from Carter on the more important West Bank settlements.

Throughout his speech, he repeated the unyielding approach he had taken in interviews and speechs in the United States just after the accords were released, detailing again how he had forced Carter and Sadat into backing down on key points.

Israeli officials say they feel that the administration "blew the dispute out of proportion by bringing it into the open just as Secretary of State Cyrus R. Vance was leaving last week to try to get Sadi Araba and Jordan to support Sadat publicly.

While Vance was explaining to Arab rulers how hard Carter was arguing the Arab case with the Israelis, Sadat was maintaining a diplomatic silence on the issue. His only brief comment on this indicated that Begin's version of the dispute may be the correct one.

"Sadat understands that he cannot embarrass Begin before the Knesset vote on the Sinai settlements," one involved diplomat said. Israeli sources predict that Begin will write a letter on the issue after the Sinai vote that will satisfy Carter.

The Vance mission was part of an intensvie administration effort to sell the Camp David agreements to other governments rather than to any domestic constituency. Although there was early discussion of a public promotional effort by the administration at home, the current assessment by the White House seems to be that it isn't needed.