His guns spiked by Israel's invasion of Lebanon and his olive branch wilted by Arab world squabbling, Palestine Liberation Organization Chairman Yasser Arafat is facing his fiercest opposition to date from within his own ranks.

With his leadership position up for renewal in a week at a meeting of the Palestine National Council--the PLO's parliament-in-exile--Arafat has little to show for his efforts to negotiate with Jordan, to avoid outright rejection of President Reagan's peace plan and to renew ties with an Egypt still suspect because of its separate peace with Israel.

As a result, observers expect Arafat to emerge from Algiers with a new, much limited mandate, hemmed in by his friends and foes in his efforts to negotiate a settlement.

But even after the Beirut defeat and even with his close allies inside the PLO increasingly outspoken in their denunciation of his free-wheeling ways, few PLO officials think Arafat's continued leadership is in any danger at Algiers.

"He is still Mr. Palestine," one Palestinian said grumbling, "even if he has been operating without a majority from the PLO, much less Fatah," the majority organization that he forged.

The latest blow to Arafat's efforts to salvage some diplomatic gain from the ruins of the PLO's military defeat in Lebanon has been administered by the United States.

Just before Christmas, Washington had set into motion a series of delicately synchronized deadlines designed to persuade King Hussein to bring Jordan into the peace negotiations outlined by President Reagan on Sept. 1.

Diplomatic sources stressed that the success of the whole process depended on American forcefulness in bringing about the withdrawal of Israeli troops from Lebanon by mid-February.

This would show a doubting Arab world that the Reagan administration meant to push ahead with the president's plan despite Israel's rejection.

With that in mind, King Hussein said on Jan. 10 that he would announce by March 1 his decision about entering the peace talks. That stand was designed to create maximum pressure on Arafat to agree to a joint negotiating delegation and a confederation with Jordan instead of an independent Palestinian state on the West Bank, which the PLO traditionally has sought to establish.

Arafat, in turn, according to the diplomatic sources, was to confront the PLO parliament in Algiers with a difficult alternative: either accept the king's offer--considered tantamount to scuttling the PLO's dreams--or reject this "last chance," knowing that Israel was in the process of doubling the number of Jewish settlers on the West Bank.

With the talks between Israel and Lebanon showing little movement, however, there seems little prospect of a withdrawal agreement before Feb. 14, when Arafat convenes the national council in Algiers.

Some Palestinian officials here said they were convinced that Arafat may yet ask a key meeting Thursday of the expanded executive committee to postpone the national council meeting in hopes that the United States might be able to prove itself in Lebanon within a few more weeks.

Several officials expressed the hope that the United States could exert greater pressure on Israeli Prime Minister Menachem Begin and Defense Minister Ariel Sharon after the publication, expected in mid-February, of the results of the official Israeli investigation of the massacre at Palestinian refugee camps in Beirut. Those results are expected to weaken support in Israel for the Begin government.

But any further postponement of the national council meeting--dates in December and in January already had been set aside--would be considered a blow to Arafat's waning credibility and only please his many enemies, both inside the PLO and in the Arab world.

Leading the detractors are the Syrians, who fear that any improvement of PLO ties with Jordan, Egypt and the United States would necessarily be bought at the cost of their own greater isolation.

Weekly during the past month, Syrian ministers have attacked Arafat, accusing him of violating the PLO's rules and regulations.

Some PLO officials are convinced that the Syrians used Abu Nidal, the anti-Arafat renegade Palestinian terrorist, to carry out the car bomb explosion at Fatah headquarters in the eastern Lebanese town of Shtawrah last month that killed more than 40 people.

"They want to cut Arafat's throat politically," one official said, "and finish him off." Arafat has resisted similar Syrian efforts to end his leadership in the past, and some Palestinians who are angry with Arafat said they think the Syrian pressure is counterproductive.

His critics inside the PLO include not only members of the three overtly pro-Syrian groups but also the radical Popular Front for the Liberation of Palestine led by George Habash and Nayef Hawatmeh's Democratic Front for the Liberation of Palestine.

Even a significant minority within Arafat's own Fatah, especially the left wing led by Nimr Saleh, and Arafat's second in command, Khalil Wazir, better known as Abu Jihad, have been outspoken in denouncing his moderation in dealing with Jordan, Egypt and the United States. But no Palestinian has dared condemn Arafat by name.

So deep run the differences between the pro- and anti-Arafat wings that Shafiq Hout, the highest-ranking PLO official still in Lebanon, recently spoke of breaking the national council's tradition of consensus and acknowledging existence of an opposition minority.

But Arafat has so little solid to offer the council meeting that one PLO stalwart said, "There's nothing to chew on, much less split over."

"The real problem," a Palestinian official said, "is that there are few choices and they are all bleak."

Predicting "volcanic eruptions" in the Middle East and increasing tensions between Washington and moderate Arab governments, the official added, "The problem with the PLO becoming violent is that is exactly what the Israelis would like.

They invaded Lebanon not because we were a military threat but because Arafat's diplomacy was beginning to pose a serious threat to them internationally."