Not long after Jimmy Carter's election, one of his key aides was asked what he hoped would be the new administration's most signal accomplishment. Instantly, the answer came back: to make government work better.

Not a surprising response, in retrospect. After all, Carter had campaigned across the country by harping on a version of that familiar political theme, "the mess in Washington." It was not political corruption he was assailing, nor the old "throw the rascals out"rhetoric. Carter was condemning the effectiveness of the federal government itself. He was going to change it. Clearly, the public approved. It was a major reason for his victory.

But there was a memorable aspect to his aides' assessment of the hoped-for Carter presidential performance. It was a modest, tempered view of leadership expounded that day more than a year ago. They all knew, the aide said, referring to the Carter inner circle, that governing in Washington was not going to be easy. They also fully realized they were not going to reform the world, or even perhaps be able to bring about major structural changes in government. Then he said:

"Look, if we can just do enough to make citizens know that the government they see and deal with is doing better, that in itself will be a significant contribution. What I mean is if people see their mail service improving, their benefit checks coming on time, the government workers they come in contact with acting competently and courteously, then we will have done a good job."

That was a thoughtful - and practical - prescription for Carter's presidency.

Somewhere along the line that measured approach to problems of governance seemed to become lost during Carter's first year. Instant action, early deadlines and timetables, implementation of all-inclusive approaches to long-standing problems - these were the hallmarks. We were going to have, in a favoriate Carter term, "comprehensive" national programs on such difficult areas as energy, taxes, welfare, government reorganization.

Of late, a different note is being struck. It is the recognition of the limits of presidential power.

As the president said Thursday, in response to criticisms about his administration's lack of success to date: "Government doesn't have the unilteral autocratic control over some of these very difficult areas." And: "I'm certainly not disappointed at our willingness to tackle issues that have historically been difficult to resolve."

Those words came immediately after Carter had demonstrated anew that he was still tackling difficult issues - and still attempting to redeem his principal political promise. He had just spelled out a proposal to make government work better.

It's the view here that Carter's plan to reform the civil service system could turn out to be a landmark in his presidency. Indeed, that it could go a long way toward fulfilling the early hopes for his administration. That doesn't mean it's going to be easy to get his reforms approved. In fact, it's already taken more than a year of delicate and difficult bargaining and maneuvering to get to this stage. The lobbying in the days to come promises to be even more intensive.

Carter's proposed reforms strike not only at the way government workers and managers have been performing; they also threaten many sacred cow special interest groups, such as veterans organizations, that have built up powerful political relationships over the years.

But the most interesting aspect of what's been achieved so far deals with the role of organized labor. Until the very day that Carter made his reorganization speech last week, union and government officials alike were privately stressing how sensitive the issue is.

"Quite frankly, and very simply, we could be skewered," one union official said. "This whole thing is a very fearful process, and from our point of view there are a lot of suspicions."

From a Carter Administration official who has taken an active role in government reorganization planning, there was concern that calling too much public attention to the labor-government dealings could jeopardize the outcome. "We feel it's too sensitive a subject to dramatize too much," he said.

What they really were implying was that a significant breakthrough had been achieved - one that would have been unthinkable only a few years before. A much-discussed and controversial plan to make it easier to fire and transfer federal workers had been given not only the backing of the largest union representing federal workers but also the tentative endorsement of the AFL-CIO's executive council.

How that was accomplished, in itself, says a great deal about the changing political climate in this country. For exactly a year top-level negotiations had been carried on between Alan Campbell, the Civil Service Commission chairman, and Ken Blaylock, who is head of the American Federation of Government Employees, the largest union representing federal workers, and Tom Donahue of the AFL-CIO's Washington headquarters' staff. In time, the talks involved Carter's domestic affairs office headed by Stuart Eizenstat and his budget office reorganization team directed by Harrison Wellford. The president, it is said, was intimately involved with the status of the discussions throughout.

Labor, understandably, was not about to approve anything that would diminish the rights and protections of its workers. In particular, labor shrinks from anything that is said to make it easier to fire employes. What labor asked for, and got, were a number of concessions - a clear backing from Carter to expand the scope of collective bargaining; a Carter pledge to create something similar to the National Labor Relations Board to oversee federal employe relations, and other promises to strengthen federal labor relations through congressional legislation.

None of this was an easy process. Other federal employe unions have been openly critical. But Blaylock and the AFL-CIO took the position that labor cannot object to an effort to improve the way government works. Its workers, after all, not only serve the government - they are served by it too.

As Blaylock bluntly said in an interview the day after Carter's speech last week: "The Civil Service does need reforming. We don't see this as an attack on our workers. We see this as an intensive, honest effort to bring about important changes. There has never been a president committee to such a program before, and we don't feel uneasy about it."

That kind of statement represents considerable change in itself.

An anniversary: This is being written exactly 45 years after the day when Franklin Roosevelt took his first oath of office and began the process that so expanded the role of Big Government - and Big Washington - in our lives. What we are now seeing is a political struggle, not new but certainly intensifying, over how to make Washington both less obtrusive and more effective. It's one of the biggest, and most critical, battles of our times, and not only for Carter and his administration.