Immobilized by the slow-motion collapse of the authority of the shah of Iran over the past year, U.S. policy-makers are depending on the Iranian army to get the shah through this crucial weekend and into a position to salvage what he can from the wreckage of his system of total control of Iran.

The salvage operation will affect vital American economic, military and political interests, but President Carter continues to resist making any moves that would hurt the shah now, even if they would improve U.S. chances to influence and perhaps moderate the eventurl outcome of the current crisis.

Carter reportedly is being advised in the strongest terms by his national security adviser, Zbigniew Brzezinski, and the U.S. ambassador to Iran, William H. Sullivan, to hew to this course.

But there is growing concern among lower-level American policymakers that the United States will have little influence on the ultimate outcome in Iran unless the Carter administration moves rapidly and visibly to pave the way for major changes in Iran's power structure.

This emerging policy battle is already sparking a fierce new round in the Washington bureaucratic exercise of finger-pointing by officials who do not want to wind up being tagged with responsibility for a potentially major policy failure.

More fundamentally, the crumbling of an another highly valued but now nationally unpopular ally has left the normally activist Carter administration trapped passively inside an increasingly familiar but agonizing dilemma of post-Vietnam world politics.

Support for the kind of covert U.S. operations that restored the shah to the throne in 1953 is ruled out as firmly as would be friendly overtures toward the opposition political forces that may bring him down now.

Committed to doing nothing that would weaken the shah in a critical testing period, the Carter administration finds itself committed to doing nothing at all for the time being.

This dilemma was underscored last weekend as the administration silently watched the failure of the shah's last chance to find a political solution to head off the impending showdown in the streets during the celebration today and tomorrow of the Moslem holy mourning days of Ashura.

Previously undisclosed direct talks between the shah and leaders of the political opposition over forming a coalition government broke down when the shah adamantly refused to yield any of his control over the army and over the national defense budget to civilian ministers in a coalition government, according to U.S. official sources.

The failure of the secret talks locked the shah and the opposition on the course of risking confrontation in the streets this weekend and for the rest of December, and pulled the Carter administration along that same path. The president could say on Thursday only that the United States would not intervene directly in any internal showdown.

U.S. officials acknowledged last week that there has been intense discussion within the administration of a more active American role in bringing the shah and the opposition together, especially on the vital question of the future of the American-trained Iranian military in a power-sharing arrangement between the shah and opposition poliicians.

That idea, and others like it, were rejected. "To discuss that in any way in Iran could invite a move against the shah by the generals now," one policymaker said. "At some point we may have to begin positioning ourselves in that direction. But that will come only when the storm dies down. For now, we have to batten down the hatches."

While this debate continues in Washington, American intelligence sources are picking up increasing signs that the Soviet Union has already decided that the shah's days are numbered and is positioning itself by its propaganda and support for Iranian groups to get on favorable terms with a successor regime.

As trouble mounted last month, the Carter administration was locked in a bitter dispute over giving official sanction to a small-scale exodus by U.S. dependents from Tehran. The Soviets quietly evacuated the families of their embassy personnel.

"Until this week, the tough decisions on Iran like evacuation just were not being made at the White House," one foreign policy analyst said. "There was total acceptance there of the overemphasis that Ambassador Sullivan is putting on any American move that might be taken as a slight to the shah right now."

Last week, the administration brought George W. Ball in to conduct a study of U.S. policy options in the Persian Gulf. This move buttressed a feeling among some policymaders that the White House had finally convluded that the shah's military government may be able to protect him through this volatile month, but not much longer.

Much of the mounting controversy around U.S. policy centers on the role of Sullivan, an extraordinarily autocratic ambassador in Laos in 1964-68 and later in the Philippines. His diplomatic reporting from Iran is described by a wide variety of U.S. government sources as being overwhelming sympathetic to the shah and his dictatorial system, and Sullivan's style is said to have sharply discouraged any critical embassy reporting that would have alerted Washington to the growing challenge to the shah.

But Sullivan has adroitly balanced this with support early this year for increased U.S. diplomatic contact with the Iranian opposition, a move that is on the diplomatic record. In the debate over dependents' evacuation, Sullivan let it be known in Tehran that he violently opposed any U.S. official involvement, but struck a far more ambiguous pose in his cables home, according to U.S. sources.

"Sullivan is much smarter than to get tagged that way,c said one knowledgeable critic. "He is n ot going to go down the tubes like Graham Martin," the source added, referring to the U.S. ambassador to South vietnam who resisted any moves toward an evacuation in increasingly desperate circumstances in 1975.

Moreover, Sullivan's sympathy for the shah is evidently shared by his ultimate boss, President Carter, who instructed one White House aide early this year to be sure that a personal note emphasizing Carter's friendship was sent to the shah on a regular schedule, according to a former administration official.