On the surface, the Reagan administration's position on the Begin government is clear. It complains about being provoked and embarrassed by the Israeli prime minister's behavior of late. But it persists in saying that despite these irritants the relationship of the United States and Israel is not far away from business as usual.
Of course the United States is insisting that the Israelis get out of west Beirut and all of Lebanon as soon as possible. And it is leaving the implication that, if Mr. Begin doesn't accede to this demand the US will feel that ''difficulties'' between the two nations are not being ironed out.
But, despite growing unhappiness over Begin-Sharon initiatives among Americans generally and among many in the Jewish community, the administration is going out of its way to emphasize the strong bond that exists between the two nations.
Further, it is clear that the President has no intention of cutting off either economic or military aid to Israel. Instead, the administration is uttering surprisingly sweet and conciliatory words, conveying the idea that one does not threaten a country elevated to the status of an ally.
Why this soft talk to the Begin government? Is this because the election is coming up and Mr. Reagan and the Republicans think this is the way to curry the Jewish vote?
Not at all. The fact is that this restrained response to Israel's excesses is part of the administration's secret strategy. It does want to see some changes in the Israeli government. But it thinks they are more likely to come about if it doesn't meddle in Israeli politics.
It has been learned that the publicly unexpressed but real position of the United States contains this rationale:
Things are working out just fine without the US making any suggestions that there should be another government in Israel. Pressures from outside and inside Israel will result in either (a) a new government or (b) a modification of the present one.
What the President is counting on is that mounting Israeli and US Jewish anger over the Begin adventure in Lebanon, and particularly the most recent episodes, will reshape the Israeli government in a direction he desires. Out of it all he sees the strong possibility now of an emerging Israeli government that will be more cooperative with the US and more responsive to his Sept. 1 Mideast peace initiative.
However, the strategy is not without risks. By reacting so moderately to Begin provocations the President may be failing to mollify the growing anti-Begin sentiment among the American people. Political writers travelling the nation these days report that many Americans feel Mr. Begin has been insulting and arrogant in his treatment of the President. They wonder why Mr. Reagan doesn't ''get tough'' with the Israeli prime minister.
There also appears to be a growing public demand that the United States withhold arms from Israel as a means of punishing Israel for using American weapons for offensive, not defensive, purposes. People across the nation who have been basically friendly to Israel over the years now say that Israel, and particularly Begin and Sharon, are getting too big for their britches.
Could it be that with elections coming on some voters will decide to vote Democratic this time simply because Mr. Reagan is looking weak in dealing with Israel?
This is a possibility. But the President is banking on there not being too much of that. Meanwhile he is playing a bigger game: global politics. And by remaining relatively restrained with Mr. Begin he thinks he is winning.