President Carter had the easy job, nursing Egypt and Israel though the long negotiations that led to their peace treaty. He left the hard part to Robert S. Strauss, his special trade representative, who has been assigned the awesome task of stimulating the Israeli and Egyptian economics.

It took Strauss only one day of his first visit to Egypt to conclude that "it is essential that we not raise expectations too high."

Before going on to Israel today, Strauss said Carter would be pleased with the "total candor, tremendous good will and desire to cooperate" that he found here, but he did not disguise his doubts about whether anything can be accomplished as fast as Carter wishes.

In a message to Congress asking more economic and military aid to Egypt and Israel, Carter said "the Egyptian government has an urgent and critical need to demonstrate to its people the economic benefits of peace.' According to Strauss, Carter's sense of urgency was so great that he insisted Strauss and his 24-member delegation of cabinet officials, congressmen, business executives and union leaders "take off right now without wasting time," even though many of them "had other plans."

Here, however, Strauss quickly learned what a long procession of American businessmen, bankers and consultants have learned before him over the past several years - that in Egypt, the American "can do" approach is like the irresistible force hitting the immovable object.

Though Egypt officially welcomes foreign capital under the "open door policy" proclaimed by President Anwar Sadat after the 1973 war, there has been little substantial investment of risk capital for many reasons. Egypt is a state-managed economy in which all public services, utilities and major factories are state owned, and the legal and attitudinal obstacles to foreign economic investment were developed over 20 years under Sadat's predecessor, Gamal Abdul Nasser.

Speaking to reporters after meeting Sadat, Prime Minister Mustafa Khalil and Egypt's leading economic officials, Strauss said, "I want to emphasize and reemphasize that the problems we are working on here are going to require tenacity and patience and creative thinking and good will."

Strauss said he has not been discussing direct government to government aid but the participation of American private enterprise in the Egyptian economy. His conclusion, he said, was that "the future of American investment in Egypt is excellent." But he coupled that with a sober warning to the Egyptians.

"American business is like business anywhere in the world," he said. "They want to support this peace initiative, but when they invest their shareholders' money they invest it for profit. They are going to go where profits can be made." Before coming here, he said, he was not sure that the Egyptians understood this, but he said he found that "that awareness has developed over the past couple of years where they never had it before."

He and members of his delegation, he said, engaged the Egyptians in "hard talks" about why American businesses have not invested in Egypt.

The basic difficulty Strauss faces is that Egypt wants and probably needs vast infusions of American and other foreign capital to get its economy moving and expects the Carter administration to come up with it while the real potential source of investment, private corporations, has other interests to serve.

Carter, Strauss said, "is very determined that this trip be the beginning of what he feels is the absolute necessity of showing that we can bring more than military hardware and some money - that we also can work together with private investment and in other ways to add to the economic stability of this area."

The United States, and he himself, are in it for the long pull. Strauss said, writing "the first two or three pages of a long book to be written over a number of years."

This first visit, he said, was essentially exploratory and would not result in any specific commitments or projects. The delegation, he said, is in Egypt "not to solve problems, not to raise expectations, but to define problems, to measure problems, to begin to provide solutions to those problems to make certain that we have measured, steady, realistic economic cooperation between the U.S. and Egypt and the U.S. and Israel."