THE Lebanese Army's forceful deployment in and around the southern city of Sidon this week brings Palestinian power in Lebanon to a new low. It also heralds a campaign by the Beirut government to press for Israel's withdrawal from south Lebanon.It is the first time the Army has been in combat since the Syrian-backed government began its drive to restore state authority throughout the country late last year. Divided Beirut was reunified; Lebanese militias suppressed, dissolved, and disarmed; and the Druze and Christian heartlands taken under Army control, all without a shot being fired. Sidon's case is different. It took two days of violent battles, involving tanks and artillery, for the Army to drive Palestine Liberation Organization (PLO) guerrillas from the surrounding hills and back into the refugee camps of Ain Hilweh and Mieh Mieh, on the city's eastern outskirts. With this action, PLO fighters have lost the freedom of movement that made the area east of Sidon a stronghold for them unique not only in Lebanon but in the entire Middle East. Preliminary estimates said about 60 people were killed in the clashes, and a larger number wounded. Many of the casualties were Palestinian guerrillas, but Lebanese and Palestinian civilians were also among those killed or injured. The Lebanese Army said it captured more than 300 Palestinian fighters. The Army's earlier successes in peacefully suppressing the Lebanese militias were made possible by Syrian political pressures and the thinly veiled threat of action by the estimated 40,000 Syrian troops in Lebanon. "We don't want to go the same way as Mich-el Aoun," says one disgruntled Christian militia official, referring to the Syrian bombing that drove General Aoun, a Christian Army chief who proclaimed himself president, from the presidential palace last October. But Syrian troops cannot operate in the Sidon area, because of unwritten "red lines" drawn by Israel when the Syrians first entered Lebanon in 1976. Israeli troops and their local proxies, the South Lebanon Army (SLA), man positions at Kfar Falous, only five miles east of Sidon. Many observers and analysts believe that, for that reason, the PLO leadership in Tunis and guerrilla leaders here - who are are reluctant to yield the PLO's last quasi-independent foothold in Lebanon - misread Beirut's declared intention to deploy the Army and to use force if necessary. It was not bluffing. The PLO had said it would facilitate the Army's deployment. But it also wanted prior dialogue with the Lebanese government on the rights of about 400,000 Palestinians in Lebanon and on measures to protect the camps. By Monday, Palestinian guerrillas had still not been ordered to withdraw back to the camps from the bases and villages they were holding in the hills. On Tuesday, Army troops advanced under a curtain of artillery and tank fire. "There was no decision on our part to fight," says a bitterly angry PLO official, explaining the rout. "Our men were sitting in their positions, waiting for orders. We wanted to sit down and talk about arrangements for facilitating the deployment. We are not just a militia, to be disarmed and disbanded just like that." The government says it does not plan to send the Army into the camps, where about 5,000 guerrillas are entrenched and, their leaders say, ready to fight "to the last drop of blood" if attacked. It took the Israeli Army and Air Force several days of heavy fighting to capture the same camps in the 1982 invasion. The Lebanese government has said that the next step after Sidon is the adjacent Jizzine area, held by the Israeli-backed SLA. But its commander, former Lebanese Army Gen. Antoine Lahad, says, "We will not withdraw from Jizzine as long as the Syrians remain in Lebanon and as long as the Palestinian and Hizbullah fighters remain active." The government does not plan to use the Army to attack the SLA and the Israelis. Its job is to control the south, so that Beirut can persuade the United States that the time has come to press Israel to give up its "security zone" inside the Lebanese border. Though the US has welcomed the Lebanese move, Israeli leaders, hostile to Syria's waxing influence in Lebanon, have shown every sign of readiness to resist such pressures.