The David Stockman sensation is now old news, and the Reagan administration's budget director would like to keep it that way. Having survived the initial storm over his indiscreet remarks in the Atlantic magazine, Stockman is now immersed in the fiscal 1983 budget, working to restore both his credibility and his authority.

For a moment last month, Stockman's closest friends in Washington thought he was finished as the administration's chief budget cutter. But Stockman hung on, and seems destined now to remain in office at least until next spring--that is, until the fiscal 1983 budget has been presented to Congress.

Whether Stockman can ever regain the stature he enjoyed during the first 10 months of the administration is a subject of ceaseless gossip and speculation on Capitol Hill and inside the Office of Management and Budget.

Stockman has improved his position markedly during the past month, according to sources in Congress and the administration. He played the central role for the White House in negotiations on the Hill over the continuing resolution that will set the limits on government spending for most of this fiscal year--and key Republicans said he played it well.

Now Stockman is in charge of preparing a new budget--the first that will be entirely Ronald Reagan's, and also the one that will be at issue in the 1982 congressional elections. "He is the chief technician, the chief scorekeeper and the chief political analyst," according to an admiring administration official who is working with Stockman on the new budget. "He has regained the leadership in the budget process.

But other sources report that appeals from Cabinet members seeking to preserve programs Stockman wants to cut are "more vigorous because of Dave's weakness after the Atlantic article," as one of them put it. And although Stockman and his staff have been emphasizing the need for continued and painful austerity, the president and his political aides have simultaneously tried to reassure mayors, governors and moderate Republicans in Congress that the new budget will not be too harsh.

In the bargaining so far, Stockman has played the traditional OMB Scrooge bent on disciplining the Cabinet members' tendencies to spend. Initially the budget director proposed harsh limits on most spending programs, but in the subsequent appeals process the cabinet has reportedly won may concessions. This is the ritualistic trench warfare of the budget season. The Reagan administration avoided it in the unusual atmosphere of last winter, but a year later the budget cutting crusade has slowed, and traditional patterns of behavior have reappeared.

With the Congressional Budget Office now reportedly preparing an economic forecast with a $210 billion deficit for fiscal 1984, some of the opinions Stockman expressed in the Atlantic are looking better and better, according to the budget director's friends.

In the article, written by William Greider of The Washington Post, Stockman said the administration's program did not go far enough to eliminate chronic budget deficits, largely because of the effects of a Reagan tax cut that was larger than Stockman wanted. Stockman also acknowledged that the economic boom predicted in last year's budget calculations was largely a product of guesswork.

Since the Atlantic article appeared, the administration has more candidly admitted that its optomistic original deficit estmates were unrealistic. Now senior Republicans on Capital Hill say it is important for the White House to produce an honest budget this time or the administration's credibility will be wiped out.

"If he Stockmanizes the numbers again, he'll be in serious trouble," a senior Republican aide in the Senate observed last week. His use of that personalized verb suggests the credibility problem Stockman now has on Capital Hill.

But the budget director also has strong support in Congress, some of it from people who were not supporters before the Atlantic flap.

For example, Sen. Mark O. Hatfield (R-Ore.), chairman of the Senate Appropriations Committee, is now firmly in Stockman's corner. According to a Hatfield aide, the senator has felt since the Atlantic article appeared that Stockman "is being persecuted for being honest." Hatfield wants him to stay.

So does Rep. Jim Leach (R-Iowa), a leading Republican moderate who has not embraced the entire Reagan economic program. Leach has publicly urged the White House to keep Stockman on. "The longer he's kept there," Leach observed with satisfaction, "the harder it's going to be for the White House to shift gears."

Democrats still hope to make Stockman's indiscretions an ongoing political issue. Rep. James Jones (DOkla.), chairman of the House Budget Committee, for example, said in recent interview: "Once Stockman comes up before the Hill, he is going to have severe credibility problems."

Jones said Stockman had not been in touch with him "since he joined the Titanic and went down in the Atlantic," Earlier, Jones said, the budget director had talked to him from time to time on budget issues.

Others on the Hill reported similar signs of a chastened, more reticent Stockman. One Senate committee staff director said the budget director now is forced to deal with aides on the Hill. "Before the Atlantic, he only met with principals," this source said.

Stockman's asociates acknowledge that he has changed his style of operating since Reagan took him "to the woodshed" over the magazine article. Stockman went on a four-day vacation over Thanksgiving, his first of the year. He has eliminated most outside speaking engagements and no longer meets with journalists. When a reporter asked the OMB spokesman what Stockman planned to say at a recent fund-raiser, the spokesman went out of his way to emphasize that the budget director would say "nothing newsworthy."

Jones predicted that the White House will use Stockman to put together and introduce the new budget, "and then sometime when Congress is out of town next year he'll quietly resign and take a good job as a corporate executive."

But he was just guessing, Jones said, and the final script will have to be written by the president. "The question is whether his confessions will have a cleansing effect" on the rest of the administration, Jones said. "Stockman alone can't control how honest the figures in the new budget will be..."

Many Republicans on the Hill agreed that the plausibility of the 1983 budget could be the key to Stockman's future.

But several also noted what seems in the end to be Stockman's best protection. As one Rebpublican put it, "There is absolutely no replacement for him in sight."