Nearing the end of his first year in office, President Carter has adopted an extraordinary low public profile in recent weeks as he grapples with the day-to-day details of presiding over the federal government.

He flew to North Carolina last weekend on a strictly private mission - to attend the wedding of his nephew - and confined his public activities to a brief interview on a local radio station. Except for weekends at Camp David, Md., it was the President's first trip out of Washington since late October.

At the White House, Carter's days have been filled with meetings, seemingly endless sessions on next year's budget, and long stretches in which there is no announced activity and when he presumably does the reading of the memos, position papers and the like that have come to dominate his presidency.

The President has stuck faithfully to his routine of two news conferences a month, but except for these and the obligatory ceremonial functions of his office he has remained pretty much out of public view. And the news conferences themselves increasingly have become listless affairs, reflecting the general atmosphere of the White House.

As for the daily White House news briefing, of late they typically begin with press secretary Jody Powell or his deputy, Rex Granum, intoning, "I have no announcements today," followed by 20 or 30 minutes of uninspired questioning and artful dodging.

Since Nov. 1, a check of Carter's public schedule shows that besides his nationally televised energy address Nov. 3 he has delivered two speeches. The first was to the World Jewish Congress meeting in Washington, an important forum in which the President delivered a prepared address outlining his policy in the Middle East.

The second, last week, was to the Business Council meeting in Washington, and if Carter considered that forum important he did not demonstrate it. He spoke, as he prefers, from notes rather than a text, rambling on for more than 20 minutes on a variety of topics and familiar themes. The business executives seemed unimpressed. Leaving the session, one of them was overheard to remark to a friend, "I wouldn't want to work for that man, would you?"

For the most part, Carter's days at the White House are predictable. Mondays, meetings with his senior staff and the Cabinet. Weekly lunches with Vice President Mndale and with Mrs. Carter. Virtually every afternoon, a long meeting on the budget as the time for hard dollars-and-cents decisions closes in on him.

It has settled into a routine and Carter, who at heart is a manager, seems confortable with it. MOreover, there is no question that what goes on in the privacy of the Oval Office - the long hours of reading and studying and sifting the details of government - are important. But there is a political price to pay for a President who so chooses to lead.

"I expected a more forceful President," one ardent Carter supporter remarked, expressing a vague but real enough disappointment.

Chatting informally the other night, Powell confirmed the general impression of a low Presidential profile. He said it resulted more from happenstance than from any deliberate plan. It is, afer all, the budget season, when any President must devote his energies to the mundane but significant nitty-gritty of his job at the expense of public demonstrations of leadership.

Stuart E. Eizenstat, Carter's domestic policy adviser, argues that now is not the time for the President to be highly visible. Rather, he said in an interview, the past several weeks have been the time for Carter to concentrate on the necessarily private hard bargaining with Congress over the year's legislative agenda.

What is most striking about this attitude is its contrast with what was being said early in the administration. It was not so long ago that political adviser Hamilton Jordan and others in the White House were speaking confidentially of using the high visibility of the Presidency to mobilize public opinion behind Carter's programs.

There were suggestions that the President would go "directly to the people" should Congress prove recalcitrant, and there were constant vows to stay close to the people.

There was a good bit of that early in the administration, but not of late. At the end of the year's great struggle over energy, Carter was not going to the people, but meeting privately with a few members of Congress, not to strike a bargain or force a resolution, but to ask them please to stick with it, to continue working diligently, as he has.

The prospect is for the President to continue with his low-profile approach to the job through the Christmas holidays, which he will spend in the privacy of his home in Plains, Ga. But no President remains too long out of public view and Carter clearly will once again become a dominant figure in the news at the end of the month, when he embarks on a trip to six countries in nine days.

About the time he returns, a White House committee headed by Vice President Mondale should be completing work on next year's administration agenda, which includes basic decisions on how Carter will use the resources and visibility of his office during the second year of his presidency.