In a Reagan-Begin showdown, who holds what cards: 2 analyses

By thrusting himself to the forefront of the Middle East struggle, President Reagan has leaped into a political high-danger zone.

His attempt to resolve the Arab-Israeli conflict has opened the way not only to new opportunities but also to new political risks for him.

The President has set into motion a long process of diplomatic action and reaction which could take not just months but years and involve more than half a dozen Middle East nations. According to a number of Middle East experts here, it is also likely to entail a major political and public-relations struggle with Israel.

The real test for President Reagan in the first few months of this long process may be his ability to withstand heavy pressure, in an election year, from Israel and from its ''lobby'' in Washington. Much will depend on public opinion in all of the nations concerned. Advisers to a number of presidents on Middle East issues have long felt that the power of an American president to persuade the American public - in the face of Israeli pressure - was one of the main weapons the United States had available in any attempt to pursue a so-called evenhanded Middle East policy.

The President has now seized that weapon as no president has since Dwight Eisenhower during the Suez war of 1957. Under the threat of US-supported sanctions, President Eisenhower compelled Israel (and France and Britain) to withdraw their forces from Sinai. If President Reagan sticks to his peace plan - and it is likely to come under some fire from all sides - it may come to rank alongside only a few previous presidential moves that left a lasting mark on the Middle East, such as the Eisenhower confrontation in 1957 and the Carter Camp David negotiations of 1978.

By eroding support for Israel in this country, the recent Israeli invasion of Lebanon has given President Reagan a degree of leeway with American public opinion and the US Congress which did not exist before. And since the invasion weakened the military arm of the Palestine Liberation Organization (PLO), the President can now argue that the Israelis are in a position to be more forthcoming in trading occupied territory for peace.

Israel has rejected the President's call for a freeze on Jewish settlements on the West Bank of the Jordan as well as his suggestion that this Israeli-occupied territory be linked with the Kingdom of Jordan.

The Israeli rejection has been taken calmly - so far - by Reagan administration officials. They apparently expected nothing less. What they are concentrating on at the moment is American public opinion, and when it comes to American public opinion, no one is considered more of an expert than Ronald Reagan himself.

A long-range target in this battle may be Israeli public opinion. Some of the experts here think that if Israel's opposition Labor Party is wise, it will see the ''Reagan plan'' as a political opening for itself. And, in fact, initial response from Labor Party leaders was cautiously favorable.

The plan is certain to set off one of the lengthiest debates ever in Israel's always-stormy public forums. It will not escape notice in Israel that Reagan's proposals are closer to the Labor Party's past proposals for peace than have been Prime Minister Menachem Begin's.

But if Mr. Begin digs in his heels, continues to build settlements on occupied territory, and is able to maintain a high level of public support in Israel, President Reagan may be faced with the painful choice of using the aid weapon against Israel. Conditions could be attached to future military aid, or at least implied. But so far administration officials are refraining from any hint of that kind of threat, knowing that it might simply unite Israelis behind their government and against pressure from Washington.

On the positive side, President Reagan now enjoys a degree of unity among US Middle East experts and among policymakers which might have been unthinkable some months ago. On every major Middle East issue until now, Reagan administration officials appeared to be sharply divided.

The hand of Secretary of State George P. Shultz is evident in all this. By consulting with a wide variety of experts and elder statesmen, he has constructed what amounts to a coalition of support for President Reagan's initiative. Administration confidence has reached the point where the President and his advisers have gotten over their qualms about former Secretary of State Henry A. Kissinger. They may even enlist Kissinger's talents in the campaign of persuasion now under way here and in the Middle East.

The consensus behind Reagan's Middle East speech of Sept. 1 even extends to former President Carter. In an interview Sept. 2 with ABC television, Carter said in response to Israeli criticisms of the Reagan plan that there is ''absolutely nothing in the President's speech . . . which is contrary to either the letter or spirit of the Camp David agreement.''

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