Can a strategic arms agreement negotiated by the Carter administration and an assertive Soviet Union at this troubled time in the history of their relations find friends and eventual acceptance in a skeptical Senate? That may be the leading political melodrama of the months ahead.

This weekend the issues in the strategic arms limitation talks (SALT) are still in a conventional diplomatic forum, being discussed by Soviet foreign minister Andrei Gromyko, President Carter and Secretary of State Cyrus Vance. But all three are now looking nervously up Capitol Hill toward the assembly its members like to call "the world's greatest deliberative body," where any SALT agreement can get peppered.

Senate rejection of a SALT agreement could end an epoch in American diplomacy and lead to radical revision of national security policy.

The Senate is unlikely to vote on a SALT agreement for nearly a year, so any judgment now on its prospects would be rashly premature. But there are senators on all sides of the issue who predict now that a SALT agreement could not be approved.

Other members and aides reject the gloomiest view as unwarranted. They see many arguments they regard as persuasive that SALT supporters will be able to advance in the debate, and they point to the popular support for arms control repeatedly evidenced in polls.

A great deal will depend on the stature and political effectiveness of the Carter administration at the time of the final SALT debate, and the skill with which the administration can manage SALT between now and then.

Another crucial but unpredictable issue is the degree to which events not directly tied to SALT - in Africa particularly - might influence a Senate vote.

One Senate aide said flatly last week, "Any idea that this treaty is going to be considered exclusively on its merits is crazy." The general state of detente, Soviet-Cuban involvement in Africa and other factors will weigh heavily, he predicted.

Edward M. Kennedy (D-Mass.) is one of many senators who take the same view.

But many of SALT's strongest proponents argue that the arms negotiations must be "de-linked" from other aspects of Soviet-American relations, since the issues in SALT are of life-and-death importance, transcending all others. According to this view, if SALT is in the U.S. national interest, that is a constant factor that doesn't change with the shifting atmosphere of superpower relations.

Several senators said in interviews last week that this "de-linking" idea is just too sophisticated to sell politically, either in the Senate or in the country.

Those who argue that the SALT agreement now being negotiated faces a bleak future in the Senate raise the following arguments:

The agreement isn't good enough. Hardline senators and aides argue that the administration that strayed too far from its initial SALT proposals of March 1977, and now proposes to allow the Soviets too many oversize rockets and a new, uncontrolled bomber system called Backfire. The agreement will leave U.S. land based missiles dangerously vulnerable, these hardliners say.

Others contend that the agreement will force the United States to undertake costly new weapons programs - a mobile landbased missile, for example - without really enhancing security and yet restricting potentially fruitful developments in other and cheaper weapons systems, like the cruise missile.

The Soviets cannot be trusted to adhere to a new SALT agreement, given aggressions in Africa, crackdowns on dissidents and other signs of persistent Soviet misbehavior. Clearly, according to this view, the Soviets are up to no good. A variation: the United States should punish the Soviets for this kind of behavior by refusing to sign a new SALT agreement.

The Senate cannot trust the Carter administration to handle the Soviets effectively, or to negotiate a reliable arms control agreement. Senators generally decline to discuss this "confidence" issue publicly, but it animates many private conversations.

For some senators the confidence issue grows from a mistrust of Paul C. Warnke, Carter's chief arms negotiator, whose confirmation in that job was opposed by 40 senators. Many senators and aides still feel that Warnke was less than candid in his testimony to the Senate, and hawks have painted him as a "softliner" who is excessively anxious to strike a bargain with the Soviets.

Others speak of the administration's "inclination to screw things up," as one southern senator put it last week. Some see a confused sequence of signals on national security issues: cancellation of the B1 bomber, then a tough speech on Soviet adventurism, then cancellation of the neutron bomb, plus obvious and unresolved differences between the calmer views of Secretary Vance and the harder liner of Zbigniew Brzezinski, the national security adviser.

J. Bennett Johnston (D-La.), the sort of middle-of-the-road southerner whose support the administration will need, said last week he would prefer to see the SALT agreement just disappear for the time being.

Johnston said that some senators who voted for the Panama Canal treaties (he did not) would like to take the conservative side of a big foreign policy issue now to balance their images at home.

A liberal senator who will support SALT noted that the extremely optimistic climate surrounding the early stages of detente in the early 1970s made it much easier to approve SALT I than it will be to get two-thirds approval for SALT II.

On the more optimistic side are a substantial number of senators and aides, with arguments of their own. For instance:

Many senators who now talk of voting against SALT as a response to Soviet and Cuban adventures in Africa will eventually realize that they are talking about a strategic issue versus a localized political one.

Moreover, many of them will eventually understand that a vote against SALT will mean a stand against negotiated arms control and in favor of a new arms race, when neither position is very attractive to the populace.

A key Senate aide said that the case for SALT and arms control has not been effectively made since Watergate debilitated Richard Nixon, but that once an agreement was on the table for open debate its supporters would again be able to remind the Senate and the country how great the stakes could be.

Sen. Gary Hart (D-Colo.), who says he will devote much of the year to the defense of SALT, went to see Carter this month to complain that the administration was doing too little to educate the country for the SALT II debate.

"Much to my consternation," Hart said, the administration wants to wait until a new agreement is complete before beginning to campaign for it, when "you really can walk and chew gum at the same time."

There are good technical arguments for the agreement. A recent meeting of generally pro-SALT Senate aides produced unexpected optimism, according to several participants, that defenders could get the best of an argument on its merits.

The SALT II pacts will require the Soviets (but not the United States) to dismantle a substantial number of existing rockets, will leave both countries with equal numbers of land- and submarine-based rockets, and will leave each side's land-based missiles vulnerable to the other's, pro-SALT sources argued.

Moreover, they said, it can be shown that the Soviets made numerous important concessions along the road to an agreement, beginning with their willingness not to consider U.S. nuclear weapons based in Europe but capable of hitting Soviet targets under the general SALT limits.

Warnke can step aside after an agreement is negotiated, eliminating a major element of the "confidence" problem. Several well-informed sources think that the White House and Warnke would see this too, and that he would return to his law practice rather than become an issue in the ratification debate.

The administration could then rely on spokesmen with harder-line reputations - particularly Defense Secretary Harold Brown - to sell SALT to the Senate.

Opposition to SALT will be bad politics. Recent public polls showed again that huge majorities favor arms control agreements. Republican senators with presidential ambitions will have to think twice before volunteering for the hawkish mantle that Barry Goldwater were into the presidential battle of 1964 with disastrous results.

Even the most optimistic senators and aides agree that none of their hopes will be born out if the Carter administration mismanages SALT. And some of them say the mismanagement thus far has been serious.

The White House is rumoured toying with the idea of submitting the SALT accords as an executive agreement that only needs majority approval, though in both houses, rather than as a treaty requiring two-thirds approval in the Senate. This deeply alarms some in the Senate who hope for SALT's success.

"I can't imagine a senior official considering that," a senior aide said. "Crazy," said a senator. "An invitation to disaster," said another.

All of them agreed that the administration has to sell SALT - and sell it aggressively - from a position of presumed strength, of clear national interest. To suggest that it oughtn't to be a treaty would invite the conclusion that the administration has conclusion that the administration has insufficient faith in the agreements, these officials said.

Friends and enemies of SALT on Capitol Hill can already cite half a dozen cases when the administration mishandled a SALT issue to its own disadvantage, and many of the friends fear that this list could grow.

An important issue in many minds is when the new agreement is to be signed. Kennedy is know to feel that it should come out in mid-October, before the fall elections so the administration cannot be accused of playing coy, but not so long before that the agreement becomes a big campaign issue.

Others feel strongly that it must be postponed until after the November voting, to eliminate any chance that senators or candidates will be forced into an anti-SLAT posture by campaign pressures.

Until lately the administration has taken the view that it should proceed as quickly as possible, and not try to time the final agreement to suit any electoral calendar. But in recent days opinion in the administration has reportedly shifted in favor of delaying the process.

The outcome of the SALT debate could easily be determined by mood and psychology.

Many senators are angry and frustrated. In the corridors one can hear again the phase "soft on communism."

One member compared the Senate today to a "guy in a bar who doesn't want to fight, but is enormously uncomfortable with the idea that everyone in the bar thinks he's afraid to fight."

Those are the makings of good melodrama.