President Reagan remained silent yesterday on the admission by budget director David A. Stockman of serious doubts about the administration's economic program in a magazine article. White House officials sought to support Stockman.

"We're all trying to rally around," one official said. "Stockman's carried so much water for the president, it wouldn't be right not to stand with him now."

While White House officials sought to squash speculation that Stockman might leave the administration because of the article in The Atlantic Monthly, Stockman ducked reporters. However, he has committed himself to appear Sunday on "This Week With David Brinkley" (ABC, WJLA), a spokesman for the program said.

Capitol Hill Democrats opened fire on the budget director. House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said Stockman had made "devastating admissions."

O'Neill said: "The architect of the administration's economic program is admitting exactly what I and other critics have been saying for six months." He accused Stockman of knowing the "fundamental weaknesses" of the Reagan economic program and choosing to cover them up.

"Mr. Stockman misled Congress and the American people as to the consequences of the Reagan economic program . . . . His credibility and the credibility of the program he supports are in serious doubt," O'Neill said.

According to the article, written by Washington Post Assistant Managing Editor William Greider, Stockman admitted in April that the economic program was not working as intended.

Stockman also is quoted as saying that the "supply-side" economics embraced by Reagan is just a new name for the "trickle-down" policies favoring the affluent that earlier Republican administrations have pursued.

When the article first circulated Tuesday, Stockman's spokesman, Ed Dale, said the article "creates an impression that is wrong and grossly misleading." Stockman is convinced the president's program "is sound and that it will work," Dale said.

Rep. Jack Kemp (R-N.Y.), one of the first politicians to espouse the supply-side theory, said, "While I cherish his friendship, I obviously must disagree with the ideas expressed in the article. They are contrary to everything Dave has ever expresed to members of the House, in public or in private . . . . Some of his friends think he has pushed himself too hard in an incredibly difficult position."

Stockman yesterday met officials on the 1983 budget to be sent to Congress in January. "He's a very resilient person. He's just going about his business," Dale said.

Deputy White House press secretary Larry Speakes said the president is being provided with excerpts. Speakes said he would not characterize Reagan as angry about the article.

Senate Finance Committee Chairman Robert J. Dole (R-Kan.) said: "I don't see anything damaging in the article . . . . I think people like a little candor in this city."