Syria's military intervention in Lebanon has turned into a deadly quagmire which holds out poor prospects for face-saving extrication and risks endangering the Camp David accords.

As Syrian heavy weapons reduce the Christian rightists' eastern Beirut strongholds to rubble, the United States, France and Saudi Arabia have taken the lead to try to work out yet another of Lebanon's countless short-lived cease-fires.

All the prime movers are trying to find a face-saving outcome for Syria. In Washington's case the solicitude deliberately disregards Syrian President Hafez Assad's opposition to the U.S. backed Camp David accords.

American concern for Assad is based on hopes he may yet join the Middle East negotiating process and on knowledge that he has shown a measure of survivability of remaining in power for eight years in a country once prone to coups.

It is also rooted in fears that the Lebanese maelstrom may tempt Israel to intervene against Syria in the name of protecting its Lebanese Christian allies.

Should that happen, Egyptian President Anwar Sadat could well fell forced to jettison his separate peace with Israel in the name of angry opinion in Egypt and the rest of the Arab world.

Assad, who flew back from East Germany yesterday to deal with the escalated Lebanese crisis, has yet to tip his hand. He has twice this year rejected redeployment plans presented by Lebanese president Elias Sarkis similar to that currently put forward by France. That was before the Christian rightists launched an all-out campaign to expell the 31,000-man Syrian force that makes up the core of the Arab League's deterrent force.

Aside from accepting the compromise, and the risk of Israeli invasion, Assad faces growing opposition abroad to crushing the Christians and a potentially dangerous course at home if he gives in too easily. His present dilemma makes a mockery of the heady days in early 1976 when Syria first undertook its gradual intervention encouraged by hopes of establishing law and order in its anarchical Lebanese neighbor.

Then Assad was solving his own problems - and those of the United States, Western Europe and most Arab countries, all delighted that Syria was undertaking a mission they chose not to shoulder. Now the Syrian harvest has become mounting casualties and reported grumbling within the army. Moreover, the West often has been willing to accept the Christian and Israeli charges of Syrian "genocide" against the Christians, especially in the light of the Syrians' heavy-handed shelling of Christian residential areas.

"It's Syria's Vietnam," a Western diplomat remarked, "but it's not 8,000 miles away. It's right next door and can't simply be abandoned."

Many Lebanese always have been convinced that Assad moved in originally in fulfillment of a longtime dream of achieving "greater Syria," a long held political concept frustrated when the French created two countries during their League of Nations mandate between the two world wars.

Other analysts believe Assad moved out of fear the anarch - which at that time could have resulted in a Palestinian-dominated left-wing government in Lebanon - would spill over into his delicately balanced country.

Although Syrian officials do not like to talk about it, Assads control reposes in part on members of his own minority Alawite Moslem sect and Syria is a country of traditionally restive religious communities.

Now two years later the leftists and Palestinians have been brought to heel. The Christians, Assad's former allies whom his troops saved from defeat then, not only have turned on him, but they also have stirred even more serious fears of contagious subversion because of their open alliance with Israel.

Open Israeli help to Christians along the Israeli border - and 130mm long-range cannon provided to those around Beirut - only confirmed Syria's worst fears.

Syrian officials feel the United States has failed to keep its part of a tacit bargain. The Syrians have controlled the Palestinians in Syria and Lebanon. The United States has failed to rein in its Israeli ally.

Yet, if Syria's apprenticeship as a regional superpower has turned sour, it has only itself to blame. Syria has forfeited its role as impartial arbiter in Christian eyes - and lost an estimated six to eight casualties a day since February - because of what some Syrians see as a major policy error committed right at the start.

Instead of establishing itself throughout Lebanon in 1976, the Syrian force deferred to its then Christian allies and did not intervene fully in their eastern Beirut and Mount Lebanon strongholds.

"Assad wanted to use the threat of force, not force itself," a young Syrian said. "We should have moved fast and fairly. That is our failure."

Even if Assad accepts the proferred compromise - and agrees to stationing Lebanese army troops between his men and the rightists in eastern Beirut - only the most extremist Christians believe Lebanon can survive without any Syrian military presence at all.

Pulling out the Syrian troops would only encourage the Christian military to partition the country - "create a second Israel" they call it here - and regenerate the civil war.

Only once has Assad deviated from the proclaimed justification for keeping his army in Lebanon - Restoring Lebanese government authority and preventing Christian-inspired partition. That was last month in a news conference during a West German visit when for the first time he mentioned that Syria might pull out its troops and let the troublesome country go its own way.

Similar feelings could prompt Assad to accept the Western compromise offer. About the only encouraging factor is that Israel has yet to signal its public support for the Christians this time. In July, Israeli jets buzzed Syrian positions and the Beirut fighting stopped.

Much of Assad's publicimage problem is written off here as the work of the well orchestrated Lebanese Christian Zionist lobbies in the United States.

"The Israelis have been so successful over the years in casting us as mad dog killers that when we are the rational ones dealing with Christian extremists they still tar us with the same brush," a Syrian intellectual lamented.