When Jimmy Carter was running for president in 1976, the man he chose as his domestic "issues" chief was scholarly 33-year-old Atlanta lawyer named Stuart Eizenstat promptly earned a reputation as a hard-working, serious staffer who was strong liberal philosophy, but not much on practical economics. "He just didn't understand the complexities," one insider says.

Today, after spending much of the earlier months in the background, Eizenstat has become a strong figure as Carters chief domestic adviser and a major influence in the administration's economic policymaking. Although little noticed outside official Washington, he's played a key role in all the major economic policy decisions the White House has made since last autumn.

"Stu isn't the Grand Vizier of economic policymaking around here yet, but there's no question he leaves an imprint on everything that comes out of here," says one white House staffer with a good feel for internal ups and downs. "And considering the magnitude of recent decisions here, that's in awful lot of clout."

Eizenstat himself describes the job as that of "a policy coordinator and neutral broker, not an economic adviser." But he adds realistically: "Obviously we give our recommendations at the end of the process." Says another official: "It's Stu's job to balance the political considerations against the economic ones. And he does it fairly and effectively."

The key question is, what's been the impact of his new role? While most of those deal with Eizenstat praise his selflessness and near-impeccable intellectual honesty, some fret that his initial lack of familiarity with key economic issues - and often stubborn adherence to traditional Democratic economic doctrine - may have hurt the administration on some occasions.

It was Eizenstat, for example, who was a key supporter of many of last year's economic policies that critics say would add most to inflation - bills to increase farm subsidies, require use of U.S. - flag ships in transoceanic cargo, boost the minimum wage and expand picketing rights for construction workers. (Both the shipping and the picketing measures failed.)

And for better or worse, it was Eizenstat who with Vice President Walter Mondale persuaded Carter to retain many of his key "tax reform" proposals in the tax-reduction package he submitted last January - over the objections of Treasury Secretary W. Michael Blumenthal and other advisers. The decision kept Carter closer to his campaign promise, but so far has helped stall the bill.

A serious-minded soft-spoken man, quick to grasp quesions and spew out no-nonsense answers, Eizenstat routinely puts in 12-hour days six days a week in his West Wing White House office, spends Sundays with his wife and family, and has no time for hobbies. Athough he grew up in Atlanta, he has only a sometime - Southern accent - and none of the good - ol' - boy demeanor of some other staffers.

An unabashed New Deal liberal, Eizenstat acquired most of his political philosophy from a liberal religious upbringing and his activist college days at the University of North Carolina. (He went to law school later at Havard.) But mainly, he learned his politics from the late Sen. Hubert Humphrey (D-Minn.) "He really was an idol of mine," Eizenstat says.

After serving briefly as a speechwriter for former President Lyndon Johnson, and later as Humphrey's research director, Eizenstat returned to Atlanta, where he joined a prestigious law firm in 1969 and he helped out - drafting issues papers - for a new gubernatorial candidate named Jimmy Carter. Eizenstat helped Carter in 1973 as well with Democratic National Committee Work.

Eizenstat's first big job for Carter as soon-to-be presidental nominee was to keep ideological planks out of the Democratic platform at the 1976 convention to give the likely candidate more room to maneuver during the campaign. Thanks to Eizenstat's softsell persuasions, the convention avoided firm stands on some more contentious economic issues. And so did Carter, later.

It is through drafting and redrafting Carter issue papers that Eizenstat says he acquired what other officials say is his uncanny ability to predict how Carter will react to a particular proposal - one of the things, besides his formal power as a coordinator, that gives him his influence over economic proposals.

The other is a mandate from Carter empowering Eizenstat, as head of the 27-member domestic policy staff, to establish the scope and timetable for all domestic initiatives - including economic policy. Although Eizenstat is credited generally with being meticulously fair in brokering other views, one official notes: "His memo still goes in on top of everyone else's."

Eizenstat has not always been a key figure in economic policymaking. In the first several months of the administration, he confined himself mostly to general domestic issues, leaving economices to the economists - primarily Charles Schultze, chairman of Carter's Council of Economic Advisers, and Bluementhal.

By late last summer, however, it was clear the economists were not going to be able to manage the show the way Carter wanted. The first effort at establishing a top economic policymaking group produced too weak a mechanism. A second, headed by Blumenthal, proved too unwieldy. With no one having seized the economic leadership, Eizenstat stepped in.

The difficulty is, for all his effectiveness, he still sometimes seems the odd man out in the administration on many key policy issues. Blumenthal and Budget Director James McIntyre both are decidedly more conservative - as is Carter, for that matter. And Schultze, an economic ecclectic, is far more pragmatic.

By contrast, Eizenstat philosophically is a classic HUmphrey liberal - with a deeply rooted belief in heavy government stimulus to spur the economy, massive new job programs and easy-money policies. Not surprisingly, his major ally in the White House has been another Humphrey protege, Vice President Mondale. The two often work in tandem.

Still, Eizenstat has tempered his philosophy some in recent months - particularly on the issue of combating inflation. "I still hold those general (Keynesian) views," he says, "but I've rethought some of my outlook, certainly broadened it. We clearly are in a new economic era where some of the assumptions have to be questioned."

Nevertheless, the staff chief's traditional instincts still emerge from time to time - occasionallly to the administration's embarrassment. Eizenstat created a minor flap a few weeks ago by publicly berating the Federal Reserve Board for its high interest rate policies - at a time when other officials were trying to work out an accord with the central bank.

To his credit, Eizenstat promptly realized his gaffe, and personally called Fed chairman G. William Miller to apologize for the incident. Still, the incident prompted chortles from other key administration economic advisers for several days. "Hell," said one later, "those weren't indvertent remarks - that's what Stu's been saying for weeks."

There also has been widespread criticism of Eizenstat's youthful domestic policy staffers, many of whom are regarded as brash and inexperienced. Both administration officials and congressmen have complained about "Eizenstat's Kid's," as the group has come to be known - occasionally provoking an intramural clash. The group was a key target at last month's Camp David retreat.

Although Eizenstat himself never has been included in such criticism, he defends his staff vigorously, without hesitation. "This is a superlative staff in terms of their capabilities." he says. They're good at carrying out the president's policies. If there's any criticism from outsiders, it's because they're doing their job." Still, the critism remains.

Eizenstat also defends the administration generally against charges that it is inept and prone to policy filip-flops. "What would have been viewed as clever and appropriate compromise if Lyndon Johnson did it is looked on today as a flip-flop," he complains. "Take the recent trimming back of the president's tax cut package. All we did was what everyone was advising."

He also discharges charges that Carter's own policies have contributed to inflation, as many economists contended last year. "Sometimes you have to choose one action because it would be more inflationary to take another," he says. And, in cases such as the recent increase in the minimum wage, Eizenstat has no apologies: "It was the right thing to do."

The question is, what kind of impact will he have over the longer run? Although top economic officials insist the White House policymaking machinery is functioning a good deal more smoothly these days than it was even a year ago, some problems still remain. And it will be Eizenstat's job to help make sure the administration can put up on a credible front. Still, no matter what he outcome, there's no question that Eizenstat, 35, has emerged as an influential force.