The flare-up that followed disclosure of a White House study proposal for taxing unemployment benefits has become a metaphor for President Reagan's political difficulties with the blue-collar coalition so crucial to his 1980 election.

But the ill-fated idea, discarded by Reagan after it touched off an uproar, represents more than a fleeting political tempest. It was also a characteristic product of the Reagan presidency, in which the chief executive is once-removed from the details of governing.

How the tax on unemployment benefits went from the drawing board to the scrap heap highlights what many administration officials view as a two-track system in the Reagan White House that does not always work and sometimes produces outright conflict.

But the episode, which had its origins in early October, also suggests that Reagan is tolerant of opposing views and controversial ideas among his senior advisers. He does not insist that his policy-makers and political associates come to agreement before they enter the Oval Office.

This tolerance by the president exists even at the risk of embarrassments such as the abortive option to tax jobless benefits, White House officials said.

It is clear to his senior staff that Reagan wants to avoid major changes in the existing White House system that seems to divide policy and politics.

Other embarrassments in the first half of his term include the proposal to give tax breaks to schools that discriminate and the quickly abandoned proposal for Social Security cuts in 1981, but Reagan has shown no inclination for a shake-up, the officials said. They point out that he has always avoided making such decisions until absolutely forced to -- a point he apparently has not reached.

In an arrangement established soon after Reagan was elected, the policy-making apparatus of the administration falls in the purview of White House counselor Edwin Meese III, while the political, legislative and press apparatus is under chief of staff James A. Baker III. Under the original plan, the Meese side would make policy, and the Baker side would steer the politics of putting it into effect.

But the scheme has not worked that simply. In the latest episode, as in previous ones, each side frequently complained that the other was not singing in harmony.

Said a Baker associate: "There is never a political review of an idea to see whether it is workable legislatively, with the press, what the political ramifications are. Things get to a formulated stage before the political side gets a shot at it. Or, it might only be a 48-hour shot."

Said a Meese associate: "The political people don't come to us very often and say, 'drop option 3.' We're looking for a range of options. We don't sit here and say, 'That's controversial, don't tell the president.' "

In the case of the proposal to tax jobless benefits, both comments contain some truth. A review of the process that gave birth to the proposal suggests that no one on the White House senior staff was kept entirely in the dark about the option. In fact, it was heatedly debated within the White House but not in Reagan's presence.

The president went to his California ranch Nov. 23 without having been briefed on options for combatting unemployment. Only after White House spokesman Larry Speakes candidly answered reporters' questions about the idea in Santa Barbara did Reagan personally intervene.

The episode had been quietly unfolding since the White House became concerned in September about the possibility of lingering high unemployment. Martin Feldstein, chairman of the president's Council of Economic Advisers, is said to have warned White House officials to expect high unemployment "for years."

On Oct. 5, the Cabinet Council on Economic Affairs was given a broad update on the jobless situation, and a staff-level "working group" soon started searching for possible Reagan initiatives. Cabinet councils fall under Meese as policy instruments, but other White House officials on the political side are frequently kept abreast of what the councils do and are invited to send representatives.

The objective in this case was to ready unemployment proposals that the White House could present to Congress in the lame-duck session.

An administration official, who declined to be identified, said Feldstein brought the "most thoughtful material" to the working group. He had published a 1973 essay in the journal, The Public Interest, suggesting, among other things, that tax-free jobless benefits encouraged the unemployed to remain out of work longer. "Further improvement in the jobless situation could be achieved if unemployment insurance benefits were taxed in the same way as other earnings," he wrote.

Feldstein made a similar argument as the working group met three more times in October. "Taxing unemployment benefits was on the drawing board," one official said. Such benefits are taxed above a family income of $18,000 a year or $12,000 for an individual; Feldstein proposed reducing that threshold to zero.

On Nov. 2, the president was briefed on the working group's progress but not told of the specific options.

A week later, the Cabinet council met again, without Reagan, but other Cabinet officers quickly attacked the jobless benefits tax.

Labor Secretary Raymond J. Donovan, Treasury Secretary Donald T. Regan and domestic policy adviser Edwin L. Harper "came down hard" on the idea, a participant said.

"They said it was political disaster," he added. "We couldn't believe this thing was going to go anywhere."

There were demands that the option be taken off the list to avoid political embarrasssment. But Feldstein was adamant, the source said. "He said it was a sound economic principle that had been sought by the previous administration and we should go with it," the source added. "Feldstein got defensive."

No effort was made by Meese to remove the option on taxing jobless benefits, officials said. The number of options was narrowed from 14 to eight, but this proposal remained atop the list. "We could have taken the list of 14 options and narrowed it to three" that were not controversial, said an official who works under Meese. "But that would have robbed the president of the chance to choose from among them."

The working group polished off the package Nov. 20 and sent it that weekend to most senior White House officials. The package also went to Reagan's office.

The following Tuesday, Nov. 23, five senior officials, including Meese and Baker, gathered in Baker's office. Reagan was to leave that afternoon, and the Cabinet council was scheduled to meet with him that morning to discuss the unemployment options.

But senior staff members, all of whom had copies of the proposals, "scrubbed" the jobless package until after last week's Latin America trip because, an administration official said, the 5-cent gasoline tax increase was more likely to be approved in the lame-duck session.

Reagan endorsed the tax plan later that day. But in the staff meeting, this official said, no objections were raised to the option of taxing jobless benefits, and it remained atop the list for Reagan's return.