President Reagan's latest effort to pump fresh vigor into his Middle East peace initiative faces uphill going. His pledge Tuesday to take ''all necessary measures to guarantee the security of Israel's northern borders'' is a clear attempt to draw Israeli Prime Minister Menachem Begin more actively into the Reagan peace process. Earlier, the President had given a variety of written assurances to King Hussein with the same aim in mind.
But Mr. Reagan's efforts, however well intentioned, still face numerous and serious obstacles. Among them are:
* It is by no means certain that the United States Congress will be prepared to follow through on the President's various promises, especially in the run-up to the 1984 election year.
* The Palestine Liberation Organization (PLO), meeting in Algiers, has declined to help the peace process along by giving King Hussein a clear mandate to represent Palestinians in negotiations with Israel over the future of the West Bank and Gaza.
* The revamped Israeli government shows little sign so far of doing the two things most needed, in American eyes, to get peace negotiations going: halting the construction of Jewish settlements on the West Bank, and accelerating the Israel-Lebanon troop withdrawal talks.
It is taken for granted here in Washington that only strong American pressure on all parties involved offers any prospect of achieving even the initial steps needed to get the Reagan plan of last September under way: an Israeli (and Syrian-Palestinian) withdrawal from Lebanon, together with peace talks embracing Israel, King Hussein, and non-PLO Palestinians.
In particular, American officials consider the active participation of King Hussein to be essential if Mr. Reagan is to achieve the main goal of his peace proposal - namely, a Palestinian entity on the West Bank and Gaza ''in association with'' Jordan.
Yet King Hussein, for his part, needs at least tacit approval from the PLO - a yellow light, if not a green - before he risks agreeing to join direct talks with Israel. In addition, he is reportedly demanding a freeze on Israeli West Bank settlements as a precondition of his actually entering peace talks with Israel as the head of a joint Jordanian-Palestinian delegation. And he is also considered unlikely to join such talks, which imply an eventual Israeli withdrawal from much of the West Bank, while the current negotiations over the simpler issue of Israeli withdrawal from Lebanon appear to be bogged down.
Back in Washington, some experts question whether the President has the leverage - either with Congress or with Middle Eastern governments - to fulfill his pledges.
''This administration,'' Mr. Reagan told an American Legion convention in Washington Tuesday, ''is prepared to take all necessary measures to guarantee the security of Israel's northern borders in the aftermath of the complete withdrawal of the Israeli Army.''
Such a guarantee, commented William B. Quandt of the Brookings Institution, ''if it means anything, means that in extremis we are ready to move our own forces in.'' Even with US troops on the ground, added the former National Security Council staffer, it would be hard - if not impossible - to prevent isolated Arab terrorists from slipping across the border into Israel. And shifting US Marines now in Beirut south to the border or putting other US forces in Lebanon would require congressional approval.
Mr. Reagan's reported pledges to King Hussein - including maximum pressure on Israel to freeze settlements on the West Bank and the pledge of large-scale military aid for Jordan - also run into potential roadblocks. Analysts here see little prospect that President Reagan could deflect the Begin team from continuing to build up a Jewish presence on the West Bank. Doubt also exists that Congress, traditionally sympathetic to Israel's security concerns, would approve a major military package for Jordan.
King Hussein, meanwhile, must sift through the Algiers conference of the PLO to determine what the final message to him is, concerning participation in negotiations over the West Bank and Gaza. Ambiguity may be all the King can hope for - the so-called yellow light.
''What the yellow light really means,'' said a US expert, ''is that the PLO will not approve of Hussein joining negotiations, but will not attack him while the talks go on.''
Hence, both the King and US officials want other moderate Arab states, notably Saudi Arabia, to line up behind Hussein's participation in peace talks. The Saudis, however, are playing a waiting game, unwilling to expose themselves to criticism from hard-line Arab governments until the PLO position is clear.
For the moment, the Saudis and their fellow Persian Gulf oil producers - Kuwait, the United Arab Emirates, and Qatar - have a more immediate problem. All four, at an emergency meeting in the Saudi capital of Riyadh, are deciding how much to lower the price of their oil, in the wake of sharp price cuts by Nigeria , Britain, and Norway.