How does a public uprising get going over a fairly esoteric new tax law not yet in effect?

In the case of the campaign to repeal a 10 percent tax withholding provision on interest and dividend income, it starts in a spartan room in Chicago equipped with a one-way mirror.

Last fall, lobbyists for the banking industry borrowed a technique commonly used by marketing departments and conducted "focus-group" sessions with customers.

They discovered that once people were made aware of the new law they were "affronted" by it. That, the lobbyists admit, is just what they were hoping to discover.

Then they took that latent anger and molded it into an outpouring of public wrath that buried Congress beneath a mountain of mail, gummed up the floor of the Senate for a week, generated a flash of temper from President Reagan and provoked threats of retaliation from Treasury Secretary Donald T. Regan and Senate Finance Committee Chairman Robert J. Dole (R-Kan).

The whole effort also touched off an argument over what the boundaries of fair play are when an interest group sets out to mobilize--critics would say inflame--public opinion.

In the focus-group sessions in Chicago, put together by the American Bankers Association (ABA), diverse people were assembled around a table and probed for their attitudes toward government, taxes, savings and banks. They were paid $25 apiece for 90 minutes of their time and thoughts. They were not told who paid them.

"The first thing that came out was that nobody knew this law had been passed," said Fritz Elmendorf, a public relations man for the bankers group, who was observing through the trick mirror.

"The more they learned about it, the hotter they got. They felt somehow affronted that the government was going to do this to them, that it was going to reach in and invade their savings accounts.

"We picked up a strong element of Proposition 13 the California voter rebellion against taxes feeling, and also a resentment about the big brotherism of the law. People said they didn't cheat, so why should they have to have their interest withheld," he added. "They also got mad at the banks for letting this happen. They figured something must be in it for us."

The banking industry had its own reasons for opposing the withholding plan, which is scheduled to take effect July 1. The industry doesn't want to be turned into the government's tax collector, especially not at a cost bankers say will be $1.5 billion this year alone, a figure others dispute.

But those rather narrow and self-interested arguments, the bankers knew, would not likely persuade a Congress grappling with record deficits to repeal a law designed to bring in $3 billion a year from the estimated 15 percent of the nation's savers who do not report their interest and dividend income.

So the bankers association decided to push those "hot buttons" it found in Chicago.

"If we just sat on our hands our customers would never forgive us," said Gerald Lowrie, director of government relations for the ABA.

"We really had no choice."

Around the first of the year, the ABA, working with a dozen other major trade associations in the financial industry, began placing ads in magazines and stuffing their customers' monthly statements and annual 1099 interest report forms with printed post cards to send to Congress.

Perhaps as many as 80 million such "statement stuffers" went out; no one has an exact count. The returns were dramatic. The Senate mail room reports that its first-class mail volume has ballooned from 5 million pieces in the first two months of 1982 to 9.5 million in January and February this year, with the withholding issue accounting for virtually all of the increase.

Dole, the leading proponent of withholding, complains that he's had to keep 13 people working full time for the past month to answer the nearly 450,000 pieces of mail he has received.

But Dole's complaints go far beyond that. He has accused the industry of waging a "heartbreaking . . .shameless campaign of fear" designed to mislead millions, especially the elderly, into thinking that interest withholding is somehow a new tax rather than a more effective way of collecting an old tax.

He's also hinted that he'll pay the bankers back with new industry taxes.

These attacks on the lobbying campaign, echoed on editorial pages around the country, rankle the bankers.

They turn around and finger their accusers as the ones cynically manipulating public opinion.

"The people up on the Hill know this 'bankers' ploy' is just a cover-up to divert attention from the real issues," said Al Ullman, former chairman of the House Ways and Means Committee, who is lobbying the bill for the U.S. Savings League.

Proponents of withholding "don't like to face up to the fact that the public is dead set against this thing," Ullman said.

"You can't make people spend their own money to send in post cards they don't want to send in. It's a bad law, and the vast majority of Congress knows it. The tactics of the Senate leadership in thwarting their will are outrageous."

Various repeal bills have 52 cosponsors in the Senate and more than 320 in the House.

Some attribute the numbers to the generosity of banking political action committees, which gave more than $3 million to congressional candidates in 1981 and 1982, but most credit the deluge of mail.

One ad that especially annoyed Dole reads, in large boldface type: "Warning: 10 Percent of the Money You Earn in Interest Is Going to Disappear," with the word "Disappear" fading to white.

Misleading? Perhaps. But the body of the ad makes it clear that this is a withholding scheme, not a new tax, and that therefore the 10 percent is a payment against taxes that would be owed at year's end.

The ad also notes there are exemptions for the poor and elderly, although it objects to the red tape.

A more inflammatory treatment comes from a sample speech distributed by the ABA to member banks: "Literally, the government will be picking the taxpayers' pockets." The government will be able to "loot your savings account," it says.

That compares with a passage in the 1980 Republican campaign platform, which opposed President Carter's withholding proposals: "They would literally rob the saver of the benefits of interest compounding."

The issue is confusing, ripe for exploitation.

There is a small compounding loss to savers when 10 percent of their interest is taken out during the year, and the banks have dwelt on this.

However, a taxpayer could compensate for the loss easily, for example, by adjusting his wage withholding schedule.

As a practical matter that is not a step most would likely take.

"We've got nothing to apologize for in our ads," Lowrie said.

Adds ABA tax counsel Lloyd Ator Jr.: "The best argument against the law is a technical one; it is simply not as cost effective for us to try to increase compliance as it is for the IRS. Last year's tax law gave them some new tools to do it.

"Those are the kind of arguments we make on the Hill, but you try doing that in a little statement stuffer and I can imagine people nodding off," Ator said. "You have to go with what gets people's attention."

Lowrie said that he is not especially troubled by the threats of Dole and Regan to penalize the industry, though he said he suspects that the tough talk has caused some large banks and the entire securities industry, which are lobbying other bills before Congress, to shy away from the withholding battle.

"I like to think in this country we don't have a tax policy based on spite," Lowrie said.