At a Sept. 30 meeting of President Reagan's Cabinet council on legal policy, Attorney General William French Smith startled Reagan and 25 of the most senior officials of the federal government by playing a 90-second tape recording.

On the tape was the voice of a man identified only as a government official agreeing to sell favors to an alleged drug trafficker for $200,000. The official's name was not divulged, nor whether he serves in federal, state or local government, on grounds that he is still under investigation.

But the playing of the tape climaxed an elaborate months-long campaign to overcome resistance within the administration and convince the president to set up a new drug enforcement program.

It was successful. The president, who has stressed on several occasions during this election year his commitment to combat crime, went to the Justice Department last Thursday to announce that new federal narcotics enforcement task forces will be established in 12 cities across the country.

He made the announcement even though there is still a dispute within the administration about where the program's cost of $160 million to $200 million a year will be found. But money was not the only issue on the table as Justice officials pressed their case.

In part, they stressed their case so vigorously with a presentation that also involved large colored maps and elaborate graphs and charts because they feared that White House aides whom they would not name were bent on denying Attorney General Smith credit for the program.

"They don't want the AG to look good," one Justice official said recently in reconstructing the events. "It's his program, he's fought for it. There are several there who want his job and they don't want him to look good."

"A lot of people at the White House feel there has been an end run," said another official. "The drug mavens feel [the drug problem] could be solved by education. [And the Office of Management and Budget] would like to beat us out of any dollar they can beat us out of."

The drug program is an example of the politics -- national and bureaucratic -- intertwined in almost any presidential decision, especially during an election campaign. It is also an example of the sometimes almost haphazard way in which decisions are made in this particular administration.

Although crime is mostly a problem for state and local governments, the Reagan administration has sought almost from the outset to make some dramatic strike against crime, and particularly against narcotics abuse.

The administration's first such initiative was creation last February of a special task force in south Florida task force under the direction of Vice President Bush. The various agencies involved were ordered to cooperate in a well-publicized effort to curb the open drug trafficking and violent crime that was terrorizing Miami and the surrounding areas.

Though the Florida task force made important progress in the areas of interagency coordination, drug seizures, investigations and prosecutions -- focusing public and political attention on the problem -- it also created difficulties.

The main one was how to sustain the effort. More than 300 Drug Enforcement Administration and Customs agents, along with additional prosecutors, had been drawn from other regions around the country. These reductions in manpower from other regions were causing enforcement problems back in those locations.

The task force showed that more law enforcement agents were needed and more coordination required among drug-fighting agencies. But the leadership assumed by the vice president's office could not be repeated in a broader effort, so the question arose: what next?

One answer was coming from a newly-arrived presidential adviser on drugs, Dr. Carlton Turner, who in June had been given the task of devising an administration strategy for handling the drug problem.

Turner, a scientist who had done research work on marijuana at University of Mississippi, headed a group that ended up recommending new stress on anti-drug education rather than enforcement.

Drafts of the Turner "strategy paper" bounced among the agencies during the summer with the enforcement agencies being particularly critical. DEA, according to one of its top officials, "thought it was a waste of time. Nothing new."

Justice, meanwhile, was also at work trying to pull together what officials there believed would be needed as a follow-up to the Florida task force approach. Part of the motivation at Justice came from disappointment that the Florida operation had been handed to the vice president. There were also calls for help from state and local officials, particularly those whose areas had been "raided" to make up the Florida task force.

During a July meeting on the fiscal 1984 budget, high Justice Department officials discussed with the attorney general what would be needed "to investigate and imprison 1,000 to 2,000 of the worst drug offenders." Out of that discussion came a request by Smith that they determine what each of the involved agencies believed they would need.

For example, an official pointed out, increased prosecutions would bring more convictions and greater need for prison space in an already overcrowded system. The overcrowding problem was also likely to be complicated by the Reagan administration's efforts in Congress to restrict bail and do away with light sentencing in drug cases.

In a series of more than a dozen meetings over August and early September, Justice officials worked out the general concepts. They rejected a notion to have mobile task forces roaming the country and settled on 10 to 12 fixed task forces geographically covering the entire country.

The planning was mostly confined to Justice at this stage. One Treasury official was brought in, John Walker, the assistant secretary with responsibility for enforcement, who controlled both the Internal Revenue Service and Customs. But neither the FBI director nor the DEA administrator was involved.

By Sept. 14, the plan had solidified enough to be taken to Edwin Meese III, counselor to the president. He was given an outline of what was involved, "about 10 task forces" at a cost of $160 million to $200 million, according to one official who was present. He set up the Sept. 30 Cabinet council meeting.

Unresolved either in the meeting with Meese or on Sept. 30 was the matter of money. OMB's representative had noted on Sept. 30 that the fiscal 1983 budget was already closed; therefore the attorney general's program should be postponed until fiscal 1984, OMB said. Smith argued it had to be done right away, and insisted he needed additional resources for the current fiscal year.

President Reagan said he wanted the budget problem worked out and another meeting was set for Oct. 6. Then Reagan, somewhat to the consternation of some aides, went out in an Oct. 2 radio speech and announced he was moving to "duplicate" the Florida drug task force "for the entire United States."

The money issue had still not been settled by the time of the Oct. 6 meeting, at which the attorney general insisted it should not come from existing law enforcement budgets, particularly his at Justice. According to one participant, Smith briskly said at one point of the funding, "That is OMB's problem."

But Budget Director David A. Stockman argued that the administration had to stay within the already agreed-upon fiscal 1983 budget levels for Justice. "If we break the budget," an OMB official said Stockman argued, "why shouldn't Congress?"

The president left the Oct. 6, session giving something to everyone. Justice officials were led to believe their program would go ahead, and Stockman won on the point that the money would have to come from some other fiscal 1983 program. The problem of finding the funds to reprogram was passed on for review on Oct. 13, by yet another group, the Budget Review Board made up of Stockman, Meese and James A. Baker III, the White House chief of staff.

That issue is still undecided. As of yesterday, OMB spokesman Edwin L. Dale Jr. said, "I'm confident . . . that a budget amendment will be sent to the Hill and will quite probably be offset by reductions in other appropriations requests."

But he could not guarantee that the money would not come from other law enforcement programs.