One of the first tasks that U.S. Secretary of State Cyrus R. Vance may have to perform in the Middle East is to lead the Israelis out of the corner into which they have painted themselves regarding the Syrians in southern Lebanon.

For the past week, Israeli newspapers have been running such headlines as "Border Tension Rises" and editorials have warned that "If diplomacy does not prove fruitful we are likely to hear the boom of cannon fire."

It seemed an excessive fuss to make about 500 Syrian soldiers and 10 tanks north of Lebanon's Litani River, and in certain respects the Israeli press has played up the situation for more than it was worth. Once having put its prestige publically on the line by demanding a Syrian rollback, Israel now faces the possibility that is nothing happens, it may find it necessary to make some kind of military demonstration or risk losing credibility.

Ever since the Syrians entered Lebanon last summer, it has been a cornerstone of Israeli policy that no Syrian or Pan-Arab force should be established in southern Lebanon.

In November the Israelis had made a show of sending reinforcements north of the border and warnings to the Syrians, treatening retaliation, were sent to Damascus via the Americans.

The tactic seemed to work, as the Syrian stayed in the north and let it be known that they had no intention of provoking an Israeli armed attack.

In the last week of January, however, the Syrians - as the main part of the Arab peacekeeping force in Lebanon - moved a battalion into the vicinity of Nabatiyah, a market town about nine miles north of the Israeli border.

The Israelis felt that the Syrians were trying to take advantage of the Carter administration's first week in office. The announced that the Syrian move was unacceptable and that the troops must be removed.

So far, to the Israelis embarrassment, the Syrians have not moved an inch.

The Americans have told the Israelis not to rock the boat so early on in the new administration; and the Israelis are putting their hopes on the Americans to bring about a Syrian withdrawal.No final decision will be made before Vance arrives next week. A note yesterday concerning the situation from the Lebanese government to the Americans is being taken here as an indication that diplomacy may yet win the day.

If it does not, Israel will face a decision that everyone here desperately hopes to avoid: to swallow the Syrian advance and back down or to make some show of force.

"Every additional day that passes without the Syrians moving from Nabatiyah detracts from our credibility both in the eyes of the Arab and also the Americans," the independent newspaper [WORD ILLEGIBLE] said recently. "This is something which is likely to cost us dearly because they can see that it is possible to play cat and mouse with us regarding our warnings and our redlines."

The red line beyond which the Syrian advance could trip an armed Israeli reaction has never been precisely defined. The size, weapons and composition of a force, its duration of stay and intent are all considered factors. Although the popular view is that the Litani River is the geographical line, the Israeli military would rather see the Syrians stay north of a line running from Sidon on the sea to Jezzin.

With general elections only three months, away, the Nabatiyah affair has become a political issue and the government must consider its credibility among Israeli voters. The opposition Likud Party, and such breakaway personalities as Gen. Arik Sharon, the hero of the 1973 Suez Canal crossing, are blaming the government for allowing Syria to enter Lebanon in the first place.

Another factor is Israel's credibility among its Lebanese Christian allies north of the border, who are trying to establish their own territorial zone with arms and ammunition supplies by Israel.

No one in Israel considers a single Syrian battalion to be a military threat. The fear here is that if one battalion is allowed to dig in, what is to prevent 5,000 men from digging in?

The Israelis do not want to see Syrian artillery or antiaircraft missiles established in an area that would dominate northern Galilee.

For the moment, credibility and prestige are playing a bigger factor than the militay threat and Prime Minister Yitzhak Babin, fighting for his political life, might feel the need to brandish a big stick if diplomacy fails.

The Israel press is now talking of a partial Syrian pullback to be arranged by the Americans before Vance arrives. Whatever the outcome, Vance is expected to spend part of the time he has allotted for Israel talking about the Nabatiyah flap instead of concentrating on long-range plans for peace in the Middle East.