Despite the smiles from both the United States and Jordan, time may be running out on President Reagan's peace plan for the Middle East.
Diplomats say that unless substantial progress is made in bringing Jordan and Israel into negotiations by next summer at the latest, Mr. Reagan's initiative may collapse.
No breakthrough was reported in President Reagan's meeting on Dec. 21 with Jordan's King Hussein. Indeed, no breakthrough had been expected. The Reagan-Hussein talks were described by officials as friendly, frank, and useful. Hussein and Reagan genuinely seemed to get along well.
But the king apparently is not ready to negotiate with Israel concerning the future of the Israeli-occupied West Bank of the Jordan River and the Gaza district until the Israelis show a greater willingness to give up those territories and stop establishing settlements there. Hussein has also made clear that he must have the approval of the Palestine Liberation Organization (PLO) before he enters talks.
Shortly after the Reagan-Hussein meeting, a State Department official indicated the Arabs viewed the Israelis' West Bank settlments as ''the major psychological obstacle standing in the way of negotiations.''
The Israelis, for their part, are apparently willing to talk with the Jordanians, but not on the basis of the conditions Hussein seems to be setting down.
On the positive side, Middle East analysts point out that:
* Most of the Arab nations have not rejected Reagan's plan for Middle East peace and have indeed had some words of praise for it.
* The PLO and prominent West Bank Palestinians are actively discussing Reagan's plan and seem to want to have a place in future negotiations.
* Hussein and PLO chairman Yasser Arafat recently agreed that once Palestinian territory is liberated, the Palestinians would hold a referendum on joining a federation together with Jordan.
The federation idea is part of Reagan's peace plan. In his Sept. 1 proposal, the President argued that ''self-government by the Palestinians in association with Jordan'' offered the best chance for peace. But to the displeasure of the PLO, the President opposed the idea of an independent Palestinian state. And to the dismay of the Israelis, he called for an immediate freeze on West Bank settlements. The Israelis have ignored that call.
Time may be running out on the Reagan plan, meanwhile, not only because the Israelis have continued to expand their hold over the West Bank, but also because of less tangible, but nonetheless important, factors. In the coming year , the Reagan administration may be bogged down in budget fights with the Congress. Because of the recession in the United States, its influence may be weakened. As President Reagan gets closer to the 1984 presidential election campaign, it may become increasingly difficult for him to exert pressure on Israel. If he chooses to run again, Reagan is likely to be compelled to court pro-Israeli voters.
''We very much feel a sense of urgency,'' says a State Department official. ''King Hussein came here ready to talk very, very seriously and we think that perhaps he shares our feeling of urgency.''
King Hussein has been interested in acquiring new American fighter planes and an air defense system, but American officials said that no new arms deal had come out of the King's talks here. An official says, however, that the Reagan administration agreed that the ''modernization'' of Jordan's armed forces would add to Middle East stability. Israel strongly disagrees with such assertions.
Following Hussein's Dec. 21 meeting with Reagan, it was announced that the two leaders would hold one more meeting before the king leaves here on Dec. 23. Close advisers to the two were to continue discussions over the next two days.
In a briefing for reporters at the White House immediately after the first Reagan-Hussein meeting, a senior administration official had some praise for the King. He said that ''it's very clear to everyone that King Hussein has been out in front'' among the Arabs in his support for Reagan's Sept. 1 peace initiative.