President Reagan faces mounting public concern over his policy in the Middle East. If he does not resolve the US dilemma in Lebanon, political observers say, this could prove to be his major foreign policy vulnerability in 1984.
The concern comes from both Democrats and Republicans, liberals and conservatives. American lawmakers, home in their districts during the holiday recess, are finding constituents worried about the direction of US policy. News media commentators of the right and left are urging the United States to extricate itself from the Lebanese quagmire. And many Middle East experts voice doubts about the President's strategy.
Mindful of the edgy public mood, President Reagan appears to be trying to mitigate the adverse impact of Lebanon by setting a tone of peace and conciliation in other foreign policy areas. The intent, experts say, is to show that the United States is not going to maintain new troop presences around the world or rely on force rather than diplomacy to solve world problems. Thus:
* The administration has quickly withdrawn the last combat troops from the island of Grenada even though, in the view of some, circumstances there might have warranted a longer stay.
* On Central America it is stressing prospects for negotiation as well as the work of the Kissinger commission. There are reports that the panel will propose a massive economic-aid program for the region.
* In the face of the arms control deadlock and soured US-Soviet relations, it is encouraging the possibility of a meeting between Secretary of State George P. Shultz and Soviet Foreign Minister Andrei A. Gromyko at the disarmament conference opening in Stockholm this week.
Reagan political advisers insist that the President is not basing his foreign policy decisions on political considerations. But they admit that Lebanon is a ''a potential political problem'' and indicate that the White House expects a changed situation there before the election campaign heats up.
''There is no question the public is nervous about Lebanon,'' says one key campaign adviser. ''But I have not identified any bloc of voters demanding that we get out. And I don't see the status quo continuing into the election year. Something will happen - either we get out or something different will happen, such as a de facto partition. From a political standpoint we have to watch this, but it's not as important now as the economy and other issues.''
Administration officials say the prospects for progress in Lebanon are better than the headlines and the shellings suggest. ''There are indications the Syrians do not want a major escalation,'' says one high official, ''and that Israel is interested in a long-term withdrawal to the degree that added land could be opened up and (Lebanese President) Gemayel could secure it. This is probably the toughest area in the world we have dealt with, but we're not pessimistic.''
Mr. Reagan does not appear to have much outside support for his policy. Many experts on the Middle East say they believe the United States has maneuvered itself into an extremely difficult situation.
''The President is in a bind,'' comments William Porter, a former US undersecretary of state who has had considerable experience in the Middle East. ''Things have gone so far that he won't be able to withdraw the US troops before the next election. The Israelis don't want the US to leave and neither does Gemayel. It's a miserable situation.''
Hermann F. Eilts, US ambassador to Egypt at the time of the Camp David accords and now a professor at Tufts University, describes the new US policy of strategic cooperation with Israel as a ''terrible blunder.''
''I have no problem with the concept,'' he says. ''But the timing of it, the method of the announcement, the flaunting of it, and obvious embarrassment it has caused to our friends in the Middle East - this I deplore. It will not make it easier to get King Hussein into the peace process.
''I have the feeling the administration is drifting without knowing what to do and getting sucked into a vortex,'' he adds.
Some experts say they believe the administration has a ''Kissingerian-like'' strategy but express skepticism it will work. The US objective, as they see it, is to use Israel's help to get an agreement between the Gemayel government and the Druze and the Shiites Muslims; to secure the airport; to come to some understanding with the Shiites; and to help the Lebanese Army move south as the Israelis pull back.
Then, according to this strategy, the US can say that the ''peace-keeping'' mission is over, the Lebanese government has a broader political base, and the US is therefore leaving except for an offshore naval presence and training of the Lebanese Army.
''But it may be too late for that,'' suggests William Quandt of the Brookings Institution. ''Amin (Gemayel) is skeptical of giving up some power, and the Syrians will not give up unless the regime is changed. Also, we are using military force, and you cannot achieve things with such military force. The policy is reminiscent of the late '70s in Vietnam when we would just about see the outlines of a deal and then start bombing North Vietnam.''
Public opinion polls are beginning to reflect the mood of concern. A new Washington Post/ABC News survey found an increasing number of Americans desiring a withdrawal of American troops from Lebanon. The majority polled felt the administration has no clear goals in Lebanon, and almost half said they believed the US would become embroiled in a war. Also, the vast majority opposed any idea of trying to push the Syrians out of Lebanon.