A favorite "good government" device of Republican governors in the 1960s was to persuade businessmen to perform well-publicized management studies of state bureaucracies, then report that the exercise had saved taxpayers millions of dollars. James A. Rhodes did it in Ohio, Dewey Bartlett did it in Oklahoma and Ronald Reagan did it in California.

What was good for Columbus, Oklahoma City and Sacramento will doubtless be good for Washington: get ready for the President's Private Sector Survey on Cost Control.

By the time this group of heavy-hitting corporate leaders is through, they will have spent at least $20 million (according to their leader, J. Peter Grace) to come up with ideas on how the government could do things better in 35 areas.

But the people, the money, the manpower, the telephones, the computers, the word processors, all of it, will be donated by the private sector. A foundation has been set up to accept contributions for office supplies and other expenses.

If early signs are any indication, the effort will provide a new store of catchy statistics to stick in speeches. In fact, one quote has already created some difficulty for Grace, a comment that food stamps are "basically a Puerto Rican program."

"I gave 940 figures in that speech," he said later, "and that was just one chart in 32. I said if we gave out food stamps in the rest of the country at the rate we do in Puerto Rico, the food stamp program would cost us $66 billion a year or 22 percent of everybody's income tax." He has since been sued by five Puerto Rican aid organizations charging slander, and he has called his remarks an "oratorical mistake."

James W. Nance, a retired admiral who briefly headed the National Security Council after Richard V. Allen departed, is the staff director for the effort, which has set up headquarters on the 11th floor of the new International Square building at 20th and K streets NW. Nance said he learned when he was in the Navy that if people were going to understand what you were saying, you had to reduce the numbers to simple terms.

For example, he said, "Interest on the national debt is $190,000 a minute."

Or, "If your pulse rate is 72, the U.S. government spends $19,100 every time your heart beats."

Or, "The government owns 436,000 automobiles and has 2.6 million civilian employes. That means every civilian employe can be riding in a car at the same time."

So much for catchy statistics.

Grace is the chief executive officer of W. R. Grace & Co., 53rd on the Fortune 500 list. He is a true believer in Reagan's economic policies.

"I'm not sure," Grace said, that getting a handle on government "is a mission impossible. I've always been a great believer that something that's never been tried before, like telling Col. Charles A. Lindbergh he couldn't fly the Atlantic, is something that should be tried."

Nonetheless, he said, government is so big that "I'm quite pessimistic about whether it can be fixed. It may be ameliorated, but I'm not sure it can be fixed.

"I have nine children and 11 grandchildren and I'm very concerned about their future."

The big problem with anything that gets as big as the federal government, Grace said, is that it "has a helluva time being incentivized."

Grace has set up 35 task forces, each led by three major figures from the business world, to search for incentives. The task force leaders have not been announced (although some are already at work) because they are still undergoing background checks. "Burdensome is not the word for that process," Grace said, sputtering.

The clearance procedure is supposed to make sure, as Nance put it, "that someone on the Boeing board doesn't wind up on the Air Force task force." On the other hand, Nance said, the Treasury Department has asked that its task force include a banker, and that request is being considered.

Most of the task forces will concentrate on specific departments or agencies. The two huge departments, Defense and Health and Human Services, each have multiple task forces. Other task forces will deal with subjects such as pay and personnel that cut across departmental lines.

While the big names are being recruited, staff from Grace's company and other businesses have assembled material and briefing books on departments and agencies. The Office of Management and Budget, the departmental inspectors general, the General Accounting Office and the Congressional Budget Office have been asked to suggest money-saving ideas.

"We're not going after programs," Nance said. "We don't have the competence to decide whether there should be food stamps or a CETA Comprehensive Employment and Training Act program ." But the task forces will be looking at where the money goes. Federal budgets for the past 12 years have been compiled with computer runs showing where each dollar is spent. "That makes it easy to spot trends over a period of years," Nance said.

The purpose, he said, "is to see if we can have some major impact in the next budget," which is already in the preliminary stages of preparation at OMB and the various departments. Once the task forces are at work, Grace said he expects their leaders to work in Washington between three and five hours a week for two weeks, and then two or three days the next week.

Recruiting top people, Grace said, has not been impossible, but "when you ask people to do something that will cost them time and money, then you lose people." The worsening business climate, he said, has cost him some top officials because "their companies needed them at this time." No thought is being given to politics in selecting the task forces, Grace said. "I don't know where 90 percent of these people stand."

The task force reports and a giant overall report will be completed by the fall, Grace said. Then begins the fun of watching what happens with the recommendations.