Secretary of State George P. Shultz, long regarded as skeptical about Middle East peace prospects after his bitter experience in failed Lebanon peace talks, is leading a campaign to persuade Congress and the news media that the visit here two weeks ago by Jordan's King Hussein justified a new optimism.

Other administration officials, after months of wariness toward Arab peace overtures, appear to believe that a breakthrough is possible but admit that they have not found a way to bring Israel and Jordan to direct negotiations.

State Department efforts to put an optimistic gloss on the situation have been so pronounced that the White House, apparently concerned about tying President Reagan too closely to an initiative that could fail, is understood to have told the department this week to dampen talk about hopes for a breakthrough.

The campaign of optimism began May 31 as Hussein's visit ended and Shultz devoted a news conference to an upbeat assessment of its results. The same positive message has since been conveyed to individual reporters at background briefings arranged at State Department initiative.

The White House's recent caution reportedly stems from recognition that State appears to be fighting uphill against skepticism, particularly in Congress and among pro-Israeli lobbying groups, that Hussein's newly declared concessions toward Israel have more to do with obtaining U.S. arms than with making peace with the Jewish state.

Strengthening the skepticism is awareness that the administration is about to give Congress a comprehensive study of U.S. arms-sales policy toward Arab nations. A large new arms and supplemental economic aid request for Jordan is expected to follow, although signals of strong congressional hostility have forced the administration to defer sending the arms package to Capitol Hill until at least midsummer.

The turning point in State Department thinking began when Hussein told Shultz and Reagan here that the Palestine Liberation Organization had agreed to accept U.N. Security Council Resolutions 242 and 338 as the basis for peace talks. For years, the United States has made that a condition for U.S. dialogue with the PLO.

The resolutions incorporate the concept of "trading land for peace" -- the basis of Reagan's 1982 Mideast peace initiative -- and are diplomatic code words for Arab accept w0121 ----- r a BC-06/14/85-PEACE 1stadd w0121 06-14 A29 underscore a conviction that, while predicting a breakthrough is not yet possible, seeds planted by Hussein must be kept viable amid the search for ways to steer toward actual negotiations.

"Something's happening, but we don't know what or how good it is," a senior U.S. official said in summarizing the situation.

The department also was encouraged Monday when Israeli Prime Minister Shimon Peres offered a peace plan that did not exclude possible Israeli talks with members of the Palestine Liberation Council, the PLO's parliament-in-exile, as part of a joint Jordanian-Palestinian delegation. Peres also did not dismiss Hussein's call for direct Arab-Israeli talks under Security Council auspices.

However, Peres' plan underlined sharp differences that remain between Israel and Jordan, and even Israel and the United States, about how to bring everyone to negotiations.

State Department officials, beginning with Shultz, readily cite enormous obstacles to that, chiefly the search for an "international umbrella" to cover direct Arab-Israeli talks.

Hussein has insisted that he needs the widest possible international backing to undertake talks so controversial in the Arab world. He called for an international conference that includes, if only at the opening session, the five permanent Security Council members -- the United States, the Soviet Union, China, Britain and France. But Israel and the United States strongly oppose adding the Soviets to the process.

U.S. officials have tentatively considered holding a conference that would include European Economic Community members and perhaps such allies as Japan and Australia.

But Hussein reportedly feels that other Arab states, even those considered friendly to the United States, would regard such a lineup as too pro-West. It would give radical Arab states such as Syria and Libya, allied in varying degrees with the Soviet Union and hostile to accommodation with Israel, an opening to brand Hussein as a Western puppet acting against Arab interests.

In addition, Israel is firmly against a preliminary meeting between the United States and a Jordanian-Palestinian delegation, proposed by Jordan as a means of giving Arafat and the PLO an indirect role acceptable to Washington.

Although the United States insists that it would not accept PLO members in such a delegation, Israel fears that such a meeting could initiate talks between Washington and the PLO, with which Israel refuses to talk.

Yet another major problem involves Hussein's argument that, in exchange for the PLO accepting the U.N. resolutions, the United States should publicly recognize "the right of Palestinian self-determination within the context of a confederation with Jordan."

Despite the qualifying language, both sides in the conflict regard the term "Palestinian self-determination" as synonomous with an independent Palestinian state, which Israel rejects and the United States opposes.

Despite its enthusiasm, the administration apparently has left itself escape hatches.

All recent public statements about U.S. conditions for meeting with the PLO have stressed that the PLO not only must endorse Resolutions 242 and 338 but also explicitly declare that Israel has a right to exist.

That is a very tough requirement for Arafat to meet, and some diplomatic observers believe that the United States might be emphasizing the point only to establish a reason not to talk with the PLO even if the resolutions are accepted.