PRESIDENT REAGAN'S Middle East proposals are the opening shot in a campaign to pry Menachem Begin from power.

This time isn't the first, of course, that American and Israeli governments have been in fierce conflict. It is, however, the first time an Israeli government has lost opposition support within Israel in the midst of a major foreign policy crisis. The Labor coalition opposition now sides with the Americans.

The tactical brilliance of Reagan's plan to get matters off dead center is that it isolates not the state of Israel, but its present government. The proposal exploits pre-existing political divisions within Israel. For that reason the proposal will gain support from that part of the American Jewish community that wasn't enthusiastic about Begin in the first place.

The question is whether the Reagan administration can play its hand carefully enough. It cannot let Begin appear to be a beleagured figure around whom Israelis feel obliged to rally as a matter of national survival. What this means is that Ronald Reagan, who has proven himself a master of American politics, will now have to prove that he can be a master of Israeli politics.

Reagan and his advisers knew that the Begin government would never accept a proposal to negotiate away Israeli control of the West Bank, the biblical lands of Judea and Samaria. It is the bedrock upon which Menachem Begin stands. Were Begin's concern with the West Bank merely a matter of security, the United States could provide assurances. But the Reagan proposal could not possibly appeal to a man like Begin who has made clear for his entire political career that he regards as a sacred duty pressing the ancient claim to all of Biblical Israel.

The proposal is a bold step backward to the approach that prevailed between the United States and Israel from 1967 to 1977. Until 1977, Israel was willing to trade territory for peace, even though the Israeli government maintained that substantial changes would have to be made in the boundaries between Israel and Jordan when the West Bank was returned. For many reasons, not least being Arab unwillingness to recognize Israel's existence, that approach never bore fruit.

What changed in 1977 was not Israel's security situation, but the Israeli government. The defeat of Labor scuttled any chance that an Israeli government would agree to the return of any of the West Bank to Jordan or anyone else as long as Menachem Begin led it. The Camp David accords, with the agreement of the signatories to disagree over precisely what had been negotiated, merely papered over the Begin government's determination to maintain Israeli control of the West Bank.

The Labor coalition's basic position is that Israel's only interest in the occupied territories is security-related -- that the West Bank settlements started by the Begin government are an economic drain on the Israeli treasury and an impediment to peace. Moreover, the Labor coalition voices concern that continued Israeli occupation of the West Bank will eventually lead to an Arab majority in Israel and the territories.

It's clear that a moment of great opportunity has arrived in the Middle East. The problem is that perceptions differ as to what the opportunity offers. It is a grievous wound for the Begin government that, flushed with its perceived victory in Lebanon over the Palestine Liberation Organization, it finds itself confronted with a major challenge from its principal benefactor.

In 1967, similarly flushed with victory, the Israelis sat back and waited, in Defense Minister Moshe Dayan's phrase, "for a phone call" from the Arabs. The Israelis expected that the Arabs would sue for peace and that a peace treaty, finally establishing Arab recognition of Israel's existence, would be concluded.

The phone never rang.

The Begin government, which has begun instalonling its own Arab leadership on the West Bank to replace a leadership sympathetic to the PLO, doubtless thought that it could use the next year to consolidate its control. The Reagan proposal scuttles that hope by drawing into question the long-range legitimacy of any leadership structure put in place by the Israelis.

In the past, when an American administration has been at odds with the Israeli government, Washington has not been able to find the means to prod the Israelis without precipitating formation of a united front in Israel and a corresponding outcry from the American Jewish community. This is why the current ballet is tricky business. Heavy-handed threats to cut off foreign aid or to cut off or suspend arms shipments may only provide the Begin government with an opportunity to rally popular support in Israel for the government's position. The last thing the administration needs is to translate this into a question in Israel of "Reagan or Begin?" For it is Israeli public opinion that the United States needs to turn the Begin government out and realize the Reagan-Labor objective.

Showing too much regard for the Labor coalition also won't work. Rather, it will be perceived as unwarranted meddling by the United States in an internal Israeli matter.

Yet sitting back and letting events take their course may let the moment slip past without exploiting it. In the months preceding the 1981 Israeli election, when the Begin government's popularity was sliding in public opinion polls, the principal cause of public disenchantment was the economic austerity measures introduced by to bring some order out of Israel's fiscal chaos. Israel attempted, with some minor success, to pry more aid out of the United States.

Faced with its own domestic budgetary problems, it may be that the Reagan administration would give some thought to reducing the economic assistance that it extends to Israel, leaving the military aid intact.

What ought to be clear -- especially to supporters of Israel in this country -- is that the way the Begin government wants to go with the occupied territories is a road that will only increase Israel's isolation in the short run and compound Israel's internal problems in the future.

For its part, the Labor coalition also needs to be equal to the moment. If the Reagan plan has any chance to work, the Labor opposition needs to overcome its own considerable problems, assert itself intelligently and to speak with a voice that the Israeli electorate will hear.

None of these steps will guarantee success. The Begin government enjoys considerable support in Israel and its West Bank policy is a deeply held article of faith for a strong and assertive segment of the Israeli public. Still, just as Anwar Sadat's visit to Jerusalem could not have been predicted 12 months before it occurred, the chance for success of this latest initiative cannot be dismissed.