In making his pitch for the President to attend the Brezhnev funeral Secretary of State George Shultz soon began to see he was getting nowhere. With a smile, he remarked that he could see that he was like a fish trying to swim upstream. Whereupon Mr. Reagan, laughing, told Mr. Shultz that he was ''more like a fish trying to leap back up Niagara Falls.''
Not only had Mr. Shultz recommended the trip. This was almost a unanimous proposal from the President's foreign policy aides, including national security adviser William Clark.
But one White House observer in a position to watch the decisionmaking process says that the President had made up his mind from the very outset that this was not the moment to take what some were calling an opportunity to forward the peacemaking process.
Mr. Reagan's decision was not, as some analysts in the media have described it, based on an anxiety that he might find himself in a position that would embarrass the United States. He expected that he would be treated at least correctly.
Rather, Mr. Reagan is pictured as having his feet ''set in concrete'' with respect to the conditions that must precede any meeting with Soviet leaders. He wants to be certain that real results ensue, that some agreements will actually be decided upon. Thus he insists that preliminary negotiations precede such a get-together, with understandings and pacts ready to sign before he sits down with the Soviets.
Had the President already met with Brezhnev and come to some amicable and useful agreement on controlling nuclear arms, then, it is understood, he would have given more consideration to going to the funeral.
Mr. Reagan is a veteran negotiator from his days as a union leader. He could envision the Soviets using his visit as an opportunity to try to impress him with a display of their armed might. He thought that pictures might well be taken of him that would be interpreted to the Russian audience as indications of US approval of the Soviet system and what it is doing.
But he likely would have taken that chance had he already had his first summit meeting and felt that he and Soviet leaders were making some progress toward cooperation. Instead, of course, he had just heard a belligerent Brezhnev rattling arms in a speech to the Soviet generals.
It seems that much can be learned about the President from his decision to skip the funeral. It is understood to be reflective of a leader who is cautious in dealing with foreign leaders and particularly so with those whose attitudes toward the US appear to be less than friendly.
Thus, while there has been much speculation of late about a Reagan visit to Peking, it now appears that it is quite unlikely. Certainly no such trip is in the planning stage.And, again, unless Mr. Reagan feels certain that something substantive is already in place, he will not visit mainland China.
Mr. Reagan is pictured, too, as becoming increasingly cautious - and suspicious - of Menachem Begin as he finds him more and more difficult to deal with. One associate describes the President's ''jaw tightening'' whenever Prime Minister Begin's name is mentioned these days.
The President's guarantee to back the existence of Israel remains firm, of course. But Mr. Reagan is increasingly unhappy over Mr. Begin's hostility toward his Sept. 1 Mideast peace initiative. And while at a recent press conference the President made no threats about applying sanctions to Israel for its continuing settlement of the West Bank, he did leave the door open for doing precisely that.
Indeed there is at least one sanction proposal now coming out of the State Department that the President is looking at: that the US cut back on aid to Israel in direct proportion to the cost of subsidizing new settlements on the West Bank. That subsidy is said to be about $100 million a year.
The President is, it seems, in a mood to ''get tough'' with Mr. Begin the next time they meet. He is understood to feel that widespread misgivings about the Israeli leader within the US Jewish community strengthen his hand in dealing firmly with him. But associates say he still will move very cautiously when it comes to cutting back on US aid to Israel.