Former budget director David A. Stockman said in an interview to be broadcast tonight that the White House vow in 1981 to protect a "social safety net" of domestic spending programs was a hastily conceived promise that could not be kept.

In an interview with William Greider for "Frontline" on the Public Broadcasting Service, Stockman said he knew that the administration could not provide a "safety net" and balance the budget at the same time because it "defied arithmetic, wasn't true."

Stockman also said top White House officials were aware that their optimistic 1981 economic forecast was not valid in June of that year -- and that deficits would skyrocket -- but decided to "sweep this issue under the rug" so as not to disrupt the political climate for President Reagan's cherished tax cut.

This and other points are included in Stockman's book on his White House years, "The Triumph of Politics: Why the Reagan Revolution Failed," which is to be published Wednesday. A second installment of excerpts of the book, for which Stockman received $2.3 million, is published this week in Newsweek.

The former budget director criticizes the president and many of his top advisers in the book, and he continued to do so in the interview with Grieder, a former assistant managing editor of The Washington Post who wrote the controversial 1981 Atlantic article on Stockman.

In the interview, Stockman singled out Donald T. Regan, the former treasury secretary and now White House chief of staff.

Regan, Stockman said, was a "profoundly destructive influence" on the president. Stockman said the advisers should have told the president early in the first term that the budget was so out of balance that "the only choice we have remaining" was a tax increase.

"We desperately needed that," he says. "Jim Baker was willing to go along. I knew it was necessary. From time to time, [Edwin] Meese would even support it. And yet, invariably, Don Regan came in and told the president, stand pat, these deficits are going away, these numbers are exaggerated, they're not real, don't raise taxes. And I don't think anybody who could add would come to that conclusion. And yet time after time, he did."

On the "safety net" issue, Stockman was referring to the White House statement in February 1981 that seven basic social welfare programs would be protected from budget cuts. Stockman said the statement was an effort to deflect a frenzy of criticism that Reagan's program was unfair to the poor and disadvantaged.

The biggest program in the "safety net" was Social Security, which Reagan had promised in his 1980 campaign not to tamper with. He later sought some benefit cuts in Social Security.

Many critics have since claimed that Reagan shredded the "safety net," which also included Medicare; school lunch and breakfast programs; Supplemental Security Income for the aged, blind and disabled; assistance for disabled veterans; Head Start, and youth jobs.

Stockman said the "safety net" promise took shape after a Cabinet meeting at which Reagan's first budget was being discussed in February 1981. While some White House aides wanted to issue a press release making the promise, Stockman says he argued against it, saying the programs "were going to have to come under the knife."

But the statement was written anyway with "a Philadelphia lawyer's fine print in it. It didn't say these seven programs wouldn't be cut, it just said the basic benefits would be protected . . . . The fine print got ignored . . . . Out of that came the idea of the social safety net and the misleading concept that a huge chunk of the domestic budget didn't have to be cut and we could still get a balanced budget. Well, this defied arithmetic, wasn't true."