Even if George Shultz pulls off the Herculean feat of arranging an Israeli-Lebanese agreement on withdrawal of Israeli troops from Lebanon, his mission will be far from over.
The US secretary of state will still have to seek a final seal of approval in the Syrian capital of Damascus from a man and a government totally at odds with United States policy and strongly backed by the Soviet Union.
If Syrian President Hafez Assad feels the pact allows Israel continued influence in Lebanon that would threaten Syrian interests, Syrian troops will remain in Lebanon. This, in turn, would block any scheduled Israeli pullback.
''If the US obliges the Lebanese government to yield to any Israeli conditions, our troops will stay in Lebanon,'' said Syrian Information Minister Ahmad Iskander Ahmad in an interview.
The Syrians' confidence, moreover, will be boosted by their belief that should diplomacy fail and another Israeli-Arab war erupt, they will have backing from their Soviet ally which has rearmed and resupplied them since last year's war in Lebanon.
''There was recently a firm Soviet Union warning to Israel that if they attack Syria, Syria will not be alone,'' said Minister Iskander Ahmad.
The Syrians, who maintain contact with the United States Embassy in Damascus, have made it clear that Mr. Shultz is welcome to come here to hear their views. They have also indicated in public and in private to the US that they would be willing to withdraw their approximately 40,000 troops from Lebanon - so long as they felt their influence there was not curtailed nor their security threatened by continued Israeli influence in Lebanon.
''I assure you when Israel withdraws unconditionally from all Lebanese territory there is no problem about a pullout between Syria and our brothers in Lebanon,'' insisted the information minister.
Syrian troops arrived at the invitation of the Lebanese government in l976 as part of an Arab peacekeeping force to intervene in the Lebanese civil war. But the mandate for this force has expired. Most of the troops are located in the Bekaa Valley in eastern Lebanon which controls the gateway from Lebanon to Damascus and thus is considered critical to Syrian security. Syrian officials are convinced that if US diplomatic efforts in Lebanon fail, the US is willing to give Israel a green light for another war in Lebanon - this time in the Bekaa Valley against Syria.
Mr. Shultz will have a tough time reconciling Syrian visions of a Lebanon agreement with those of Israel. Syrian officials are deeply skeptical of US intentions. They insist Israel should not be ''rewarded'' militarily or politically for the war in Lebanon by any continued military presence there. This includes residual troop presence, reconnaissance overflights, joint Israeli-Lebanese patrols in south Lebanon, or an important role for the Israeli-backed south Lebanese militia of Maj. Saad Haddad. Israel has insisted on all of the above and more.
Lebanese President Amin Gemayel - in constant touch with Syrian officials - this week has taken a tough line. He has insisted that only Lebanese Army troops should patrol the south, though the Lebanese are willing to accept a joint Lebanese-Israeli-American supervisory committee in southern Lebanon. The Syrians do not appear in a mood to compromise. ''When there is an agreement reached and we read it in detail we will give our clear sentiment,'' said Muhammad Haydar, head of the foreign relations bureau of the Baath Arab Socialist Party.
Nor are the Syrians displaying enthusiasm for reported US proposals brought by Mr. Shultz for US ''security guarantees'' for Israel in south Lebanon. The Syrians view any wider US role in Lebanon in the context of US aims to expand its Mideast influence while excluding Syria's ally, Moscow, from any negotiating role.
They see the Shultz mission as an effort to boost sagging US credibility - a must for reviving the Reagan Mideast peace plan. But Syria wants both great powers included in any wider peace effort and sees little reason to facilitate rejuvenation of the Reagan plan.
The US has little leverage with which to win the Syrians over. One hope is that moderate Arab states, especially Saudi Arabia, will pressure or reward Syria to withdraw from Lebanon. But the Syrians believe that the moderate Arabs, fearing a possible new war with Israel and seeing the continued US inability to modify Israel's hold on the West Bank, will keep up their support for Syria.
Nor are the Syrians impressed with a letter recently sent by President Reagan to Mr. Assad reiterating US policy that United Nations Resolution 242 implies return of Syria's Golan Heights, occupied by Israel, in exchange for peace. Syrian officials say the US words are neither new nor backed up by actions pressuring Israel.
Finally, even the threat of war, if Syria remains in the Bekaa, is not sufficient to deter the Syrian stand. Syrian officials admit they would not win another conflict with Israel. But they express confidence that Israel would pay a much higher price than it did last June, while emphasizing Soviet support for their position.