At a meeting of the Senate Foreign Relations Committee last week, Secretary of State Cyrus R. Vance and Defense Secretary Harold Brown were being pelted with praise for the Carter administration's success with the Egyptian-Israeli peace treaty.

Then, committee Chairman Frank Church (D-Idaho) suddenly threw a fast ball.

"There's something that's been generating a lot of smoke lately," he told the two Cabinet members, "and I want to know if it's connected to any fire."

Specifically, Church said, he wanted to ask whether administration strategists are measuring Egyptian President Anwar Sadat for the mantle in which the deposed shah of Iran had tried to wrap himself, that of a pro-western gendarme for the turbulent Middle East.

As Church noted, the idea has caused a lot of speculation, so much so that one bit of mordant black humor currently making the rounds of diplomatic circles asks whether Washington wants Sadat to change his name to Shahdat.

It's a joke that White House and State Department officials don't think is very funny. To them, it's loose talk that ignores such realities of the emerging U.S.-Egyptian relationship as the limits on Washington's ability to underwrite Egypt's military muscle-flexing and Sadat's innate nationalistic reluctance to become the client of any superpower.

That's essentially what Brown and Vance told Church. While conceding that there may be a role for Egypt in advising and assisting smaller countries in the area. Brown said, "it's not our intention to use any state in the region as a U.S. pawn."

But, despite Brown's denial, that's precisely the sort of speculation heard in diplomatic and military circles since late February when Sadat gave him a militaty shopping list that U.S. officials described as involving "billions upon billions of dollars."

With such an infusion of U.S. arms, Sadat reportedly told Brown during their meeting in Egypt, his armed forces could act as a stabilizing military force in an area stretching from Algeria to Afghanistan.

Since then, the speculation has been given fresh impetus by the peace treaty, which has estranged Sadat, at least temporarily, from his traditional allies in the Arab world and has underscored the degree to which he must rely on U.S. diplomatic, military and financial backing.

The persistence of discussion about Egypt as a potential client-state, military bulwark of the United States has prompted Church, even before last week, to warn publicly about "dangerous, 'pie in the sky' talk of making Egypt another Iran."

"We should have learned from our experience in Iran that nothing could be more foolish than to try and make Egypt a Middle Eastern military surrogate," Church says. "The last thing we want to do is build up a new military colossus out there and then find it turning out like Iran, with Sadat no longer president and the whole place in chaos."

His warning doesn't provoke any arguments from administration policy makers. While making no secret of their hope that Egypt will become an increasingly dependable ally and a force for stability in the Middle East, they also insist that the administration has no intention of trying to nominate any country as the regional successor to Iran.

Instead, administration sources say, the thrust of U.S. Middle Eastern policy will be to cultivate informal but close ties with a number of key countries-Israel, Saudi Arabia and Jordan as well as Egypt that share the general western goal of stability in the region whose geographic position and oil resources are so crucial to world order.

To bolster these ties, the sources add, Washington is planning a number of initiatives, such as a more visitable U.S. military presence, to give pro-western governments a greater sense of self-assurance, and beefed-up infusions of American aid to help friendly countries deal more effectively with their internal problems.

Within this context, Egypt, as the largest and most military powerful country of the Arab world, is obviously of vital importance to American planning. And, while U.S. officials wince visibly at the suggestion of a "client-state" relationship, they concede that keeping Egypt on track toward peace with Israel and good relations with the West will require a very high degree of U.S. money and moral support for Sadat.

As the leader of a desperately poor country plagued with all the classic symptoms of underdevelopment, over population and low life expectancy, Sadat urgently needs a wealthy patron able to help him make good on his promises of modernization and a better life for his countrymen.

Having made a decisive break with the Soviet Union, which long acted as Egypt's military and development mentor, he now is looking pointedly to Washington to take up some of the slack.

Specifically, there are three areas - diplomatic, military and economic - in which Sadat wants a lot of American help, and U.S. officials, while anxious to accommodate him as much as possible, say frankly that each involves some potentially sensitive problems.

Of the three, the diplomatic problems are the most immediate. Because the peace treaty with Israel has isolated Sadat from the other Arab countries, Sadat needs Washington to run interference for him in his drive to regain Egypt's good standing within the Arab world.

In part, that means the use of U.S. influence to try to heal the breach with countries like Saudi Arabia and Kuwait, whose oil wealth has helped to keep the Sadat government financially afloat.

Even more importantly, Sadat clearly expects the Carter administration to help him get an acceptable resolution of the next stage in the Middle East peace process: negotiation of political autonomy for the Palestinian inhabitants of the Israeli-occupied West Bank and Gaza Strip.

Utimately, Sadat's only hope of recapturing influence within the Arab world depends on convicing suspicious Arab governments that he can solve the Palestinian problem through negotiation rather than confrontation with Israel.

But a solution widely acceptable, to the Arabs is almost certain to involve concessions beyond what Israel is prepared to make. While it is too early to tell which way the West Bank-Gaza negotiations will go, some U.S. officials fear they will produce conflicts that could cause Sadat to expect President Carter to put pressures on Israel greater than what is politically feasible for an American president.

In terms of military support, U.S. sources say there is absolutely no likelihood of a wholesale American refurbishing and re-equipping of the Egyptian armed forces along the lines suggested by Sadat to Brown in February.

Sadat, they note, has genuinely legitimate concerns about the geopolitical implications of the chaos that hit Iran spreading through the Middle East and leaving Egypt isolated in a sea of hostile, radically oriented states.

But, the sources add, Egypt's geographic, political and financial circumstances are so different from those of Iran that Sadat has no logical hopes of aspiring to the kind of policeman's role that the shah tried to carve out for himself.

For one thing, Sadat lacks the vast oil wealth that enabled the shah to pay cash for modern, sophisticated weaponry. Even the one significant U.S. Egyptian military deal that has been arranged so far, the purchase of 50 American F5 jet fighters, is dependent upon the still unclear question of whether Saudi Arabia will pick up the bill for Sadat.

Beyond that, any further large-scale transfers of U.S. weaponry to Egypt would have to be outright gifts. And, the sources say, there is no chance of such largesse being approved by Congress, which is still smarting from the experience of Iran and concerned that the balance of Israel's military superiority over Egypt not be disturbed until it becomes a lot clearer that the Egyptian-Israel peace is going to stick.

These realities have been made clear to Sadat, the sources say, and the indications are that he had accommodated his expectations of military aid to them. But the sources add both the administration and Congress are sympathetic to the argument that Egypt does have some legitimate military needs and that the United States should be receptive to more modest, scaled-down requests.

Much of the Soviet equipment on which the Egyptian forces are largely dependent is outmoded or in need of replacement, and the United States is actively studying ways to help the Egyptian military increase its defensive capability to deal with potential threats from neighbouring countries like Libya and the Sudan or in sub-Saharan areas like the Horn of Africa.

As a first step in this direction, Carter, acting under commitments made to Sadat during the treaty negotiations, is asking Congress for a supplemental appropriation of $1.5 billion in military sales credits for Egypt.

While there is no likelihood of U.S. military assistance climbing to the billion-dollar-a-year level provided to Israel, U.S. sources predict that arms aid to Sadat will continue to increase and eventually make Washington the principle supplier of the Egyptian military.

There is also the question of economic and development aid, and while it hasn't received as much attention as military assistance, many administration sources think this is potentially the most important area of greater U.S.-Egyptian cooperation.

That attitude also stems from the experience of Iran. As one State Department official put it: "An army of 700,000 men with the best weapons money could buy wasn't able to save the shah when he got out of tune with the desires and aspirations of his people.

"Thus," he continued, "our advice to any Middle Eastern leader is to know what his people want and convince them that he's trying to give it to them. We think that Sadat, in pursuing peace with Israel, was responding to what the Egyptian people wanted, and we think we now have to try to help him to take the next step: using the peace to look inward at Egypt's internal problems and solving them to provide a better life for its people."

Again, administration sources stress that the United States can't give Sadat a blank check or even underwrite a major role in Egypt's monumental development needs. But Carter's post-treaty supplemental request to Congress include $300 million for Egyptian development aid, and the sources say there'll be more to come in this area.

In the view of many officials, the big problem will involve not so much amounts of aid as ensuring that the Egyptian government uses it in ways that will tamp down potential unrest by effectively treating the country's most pressing needs.

Under a category of financial aid known as security supporting assistance, Egypt tentatively is to receive $750 million from the United States during the 1980 fiscal year, the largest single amount directed at a lesser developed country.

Recently, Roy L. Prosterman, a University of Washington law professor who does an annual rating assessment of the foreign aid program, gave the Egypt program a grade of "D."

In his study, Prosterman charged that roughly 95 per cent of the money is slated to go into projects - expensive housing, large agribusiness development and improvement of the telephone system - that he said will provide no benefits for the country's poor massess. The result, he predicted, will widen the gap between rich and poor and increase the danger of an upheaval similar to what happened in Iran.

That's precisely what the administration wants to prevent, and officials privately make no secret about what's at stake. As one Middle East policymaker sums it up:

"We want a peaceful and stable Middle East, and we can't have it unless Egypt is peaceful and stable. It's wrong and futile to think of making it a client or a military surrogate. But if we're going to achieve our policy goals in the region, we have no choice other than to convince Sadat firmly and irrevocably that a close relationship with the United States on a broad range on interests giving him a better shot at meeting his needs than any other option."