For the third straight day Israeli-backed Lebanese Christian troops were pitted today against Palestinian guerrillas in the biggest upsurge of fighting in months, threatening to undermine crucial American efforts to stabilizesouthern Lebanon.

On the line is American credibility not just in Lebanon, but in the entire Middle East, for the Carter administration is under great pressure to show that it is capable of having its will done anywhere in the region.

At the scene, it is hard to appreciate why the stakes are so high.

From this deserted village near the Israeli border, only occasional white puffs of smoke marked the barrage by Israeli or Christian artillery directed across the valley at Palestinian positions in Khiam.

Since the fighting increased in tempo Friday, each side has accused the other of launching ground attacks in a conflict that for the past six months had been largely limited to artillery duels.

There have been claims of Israeli air force strafing and bombing and massive tank deployment, but even if true, the purely military details are of only secondary importance.

What counts in what is essentially a political war is whether the present fighting will provide the different sides with reason for opposing the plans worked out two months ago to pacify southern Lebanon.

The Lebanese government, its Syrian protectors and the Palestinians basically agreed to a formula allowing the fragile Lebanese army - which has yet to recover from its disintegration during the civil war - to move into the south and replace both the guerrillas and Christian Lebanese forces.

Acting as a go-between, the United States had been trying to gain Israeli acceptance for the plan, which would provide a modicum if security for the border area in which Israel has refused to have Syrian occupation troops stationed.

The consequences of a U.S. failure go far beyond the destruction of dozens of southern Lebanese villages that have come under regular pounding by Israeli and Christian artillery in the past year.

Here, in what was until April a town of 8,000 inhabitants, some 50 civilians live among the small garrison of Palestinians and leftwing Lebanese. A Christian position at the top of the mountain ridge dominates the town.

There is no water, no electricity, no school and precious little hope.

Toward the Mediterranean, the town of Qaaqaaiyet Jisr was subjected Friday to its first artillery pounding of the war - 19 shells fell without causing any casualties. The inhabitants, many of them refugees from other villages already emptied by the fighting, wonder it Qaaqaaiyet's turn has come.

Beyond such humanitarian considerations, U.S. prestige is on the line in the larger issue of an overall Middle East peace settlement.

For as a Christian leader favorable to the southern Lebanon pacification agreement remarked in Beirut: "If the United States is not able to get the Israelis to agree to this settlement how can Washington talk about Israeli withdrawal from occupied Arab territory?"

On face value, the proposed deal should satisfy the Israelis. they have long demanded that the Palestinians be removed from the immediate vicinity of the Lebanese-Isreali border from which in the past they launched raids and unleashed artillery and rocket attacks.

But Israeli backing for the Christian in the south has prompted observers to question whether Israel is now interested in keeping boiling a situation that destabilizes not just Lebanon, but much of the Middle East.

After all, Israeli Prime Minister Menahem Begin has vastly increased his popularity at home by defying American desire in the Middle East.

"Israel provides the tanks, artillery rifles, ammunition, planning, communications, intelligence - everything but the cannon fodder," a Western diplomat noted in describing the limitations on the 1,500-man Christian force operating in two widely separated pockets near the Israeli border.

The Palestine Liberation Organization, which signed the July 25 agreement to pacify southern Lebanon, now seems to be having second thoughts, judging by the recent negative comments by its leader Yasser Arafat.

Under increasing pressure from critics inside the PLO who question his knuckling under to Saudi Arabia on reconvening the Geneva peace conference, Arafat might well find it expedient to adopt a tough stance over southern Lebanon.

American concern for nailing down Israeli agreement became clearer when U.S. Charge d'Affaires George Lane conferred six times in the past week with Lebanese ministers.

As stake were Israeli demands that the PLO reduce its strength below the already extremely limited levels permitted under the 1969 Cairo agreement between the Lebanese government and the PLO.

The Israeli demands have been resisted so far by the Palestinians, who do not want lose face by having to admit they have had to give away more than they did in 1969, and in fact have abandoned fighting along the border.

The Lebanese government would have liked Washington to guarantee the July 25 agreement, but has had to accept U.S. reasoning that the United States can have nothing to do with any arrangement in which the PLO is a direct party.

At best the United States considers itself a go-between for what would be only tacit Lebanese-Israeli agreement to stabilize the southern Lebanese situation.

Casting further doubts on the applicability of the agreement is the makeup of the 900-to-1,200-man Lebanese army force that would be stationed in the area evacuated by guerrilla and Christian troops.

The Lebanese army has yet to recover from the civil war when it split into at least four identifiable factions. Despite efforts to rebuild, even optimists worry about the durability of a force made up of mixed Christian and Moslem troops if there is any kind of showdown.

"Such an army cannot police the south staffed mostly with cowards who ran away from the fighting" in the Lebanese civil war, a recent visitor was told by Bechir Gemayel, military commander of all Christian forces.

What he did not say was that he leads an important, but minority faction amony the Lebanese Christian leadership that does not want any settlement in the south. That faction still hopes that Israel will back them to the hilt and allow the resumption of fullscale fighting to drive all 400,000 Palestinians out of Lebanon.

Western diplomats are convinced that implementation of the agreement on southern Lebanon would clear the way for a return to political stability that is lacking despite the presence of the mostly Syrian 30,000-man occupation force that has policed the 10-month-old ceasefire.

Lebanese Moslems, who came out second best in the civil war, could enter into political reconciliation talks with the dominant Christian minority because they could not be accused of betraying the Palestinians.

If the agreement on pacifications, southern Lebanon is implemented then president Elias Sarkis, in the words of one prominent Lebanese politician, "becomes a real president, not the half president of the republic or the president of half a republic."