Seven days in July.

They began last Sunday with President Carter going on television to explain what had gone wrong with the first 2 1/2 years of his presidency. They ended yesterday with Carter sitting with reporters in the White House explainig in confident tones the week that was.

It was an extraordinary week in the life of one man's presidency. It was a week in which he had most of all wanted to fire a single employee-Health, Education and Welfare Secretary Joseph A. Califano Jr. But in the process, he took official Washington through a wild roller coaster ride complete with high-placed whoops and shrieks of alarm. And when it was over, Washington's cognoscenti were left with the dizzy feeling that they had gone through something of great importance, although in terms of solving problems with policy they were getting off the roller coaster at the same point they had gotten on.

Policy, of course, is not really what the past week was about. Rebirth is actually what it was. In the serenity of Camp David, after studying the polls and listening to his counselors, Carter had come to realize that he had just about run his presidency into the ground. His only hope was to start anew.

"There had to be a dramatic and drastic change," one of the presidenths top advisers said. And that, perhaps best of all, explains the past week. Dramatic. Somehow, with his presidency mired and a reelection campaign just months away, the American public, the Congress and even the Washington-based press corps had to be made to accept the con cept that there truly could be a new Carter.

In Washington, a city that lives on perception and image, it was every bit as important to create to feeling of dramatic and drastic change" as to make the change itself.

So it was that the president did not simply ask for the resignation of Califano, the only Cabinet officer he felt truly had to go (charges: political assault and battery against the Carter inner circle, disloyalty in the ranks).

Carter suggested at a Cabinet meeting that his entire Cabinet offer to resign. In a gesture as spontaneous as the outcome of a tag-team wrestling match, the members of the Cabinet promptly fell all over themselves to say that, yes, they all would offer to resign.

When it was over, five Cabinet members were gone, but only one truly was removed. Attorney General Griffin B. Bell had wanted to resign fro some time, and everyone knew that. Energy Secretary J R. Schlesinger Jr. had tried to resign twice before (only to be asked to stay) and had gone to Carter a month ago to declare himself a political disaster area, before Carter had to go to him with the same assessment.

Transportation Secretary Brock Adams had been on the list to stay, but Carter wanted him to replace his deputy secretary and Adams chose to mutiny, thus guaranteeing his dismissal.

Treasury Secretary W. Michael Blumenthal and Carter maintain that their parting was genuinely mutual, but perhaps slightly out of sync. Carter had decided to fire Blumenthal before Blumenthal got the word to him that he wanted to resign.

The result of Carter's move to get resignation offers from his Cabinet and senior White House staff members had two effects-one anticipated by Carter and one not.

The move succeeded in creating the impression of a major overhaul of the Carter adminstration-a sort of rebirth after 2 1/2 years of governance and gestation.

But in stunning the capital, it also silenced that groundswell of support that had begun as a result of his confident pledge of leadership and action in his television speech last Sunday, and in the address last Monday in which he unveiled the third energy plan of his one presidency.

The representatives and senators who had been putting out press releases of praise began issuing statements of shock and concern.

The mass resignations hit hard in this capital where tenure is secured by those who Gallup best. But if any priase for Carter's effort was still being heard in Washington, the next event took care of that.

A new Carter job evaluation questionnaire for rating White House and subcabinet officials on performance and attitude was distributed to the Cabinet and leaked almost simultaneously to the press. The comments about the White House were transformed from the sublime to the ridicule. Republicans in Congress took to rating Carter and his staff on their own form sheet, and Democrats joined in the laughter.

The questionnaire actually was designed originally to be used for evaluating the White House staff alone. It was drafted earlier this month, during those days when Carter was conferring and contemplating in Camp David, by Michael Berman, Vice President Mondale's counsel, with the help of a Washington consultant.

The entire project was under the supervision of Carter's new chief of staff, Hamilton Jordan. When he took it to the president, Carter decided that he would like the entire subcabinet rated on the form sheet.

Even Jordan is said to be uncomfortable with one question, which asks what percentage of the employehs effort is devoted to accomplishing administration goals and what percentage is devoted to personal goals (maximum of 100 percent, please).

But Carter strongly defends the questionnaire, making no apologies for its use or its content. He believes that the overall process of reviewing the performance of the department people will be healthy, both for those being reviewed and for the Cabinet officers who are taking a closer look at the performance of the people under them.

The Cabinet, under the new Carter alignment, is not likely to produce anything new in the way of policies or directions (nor does Carter expect it to).

Patricia Roberts Harris, who is moving from housing and urban development to health education and welfare, is every bit as liberal as her predecessor, Califano, and can represent the constituencies of the poor and the needy just as well as the man who designed the Great Society programs of Lyndon Johnson.

Harris is, like Califano, feisty and outspoken. But she is outspoken with in bounds. She recently spoke before a national women's group and stauncly defdended Carter's policies on women-a move that earned her key loyalty points with Carter and his inner circle at a crucial time.

Loyalty. Team play. Every president comes to yearn for those qualities in subordinates as he comes upon hard times in his presidency. Kennedy felt the call often. Johnson was almost paranoid on the subject. Nixon made the quest a political art form.

And Carter, who is at least as embattled as any of them, has picked up where his last elected predecessor left off.

Carter's senior White House staff had come to the conclusion long ago that Califano was, more than any other Cabinet head, out to have his own way at their expense. Eventually, Carter, fed mostly by reports from his own staff, also came to that conclusion. At Camp David he concluded that one of his leadership problems was that he had not enforced a spirit-forged in the great tradition of Rockne, Lombardi and Nixon-that team play is the only way to play. He is said to believe that it even would be better to have a Cabinet secretary who was a bit less bright but totally loyal. And the explanation for all that he has done, made known forcefully and contidently to reporters yesterday, is that loyalty will rule supreme in the second Carter administration, the one that began this past week.

EPILOGUE: One of America's most influential lobbyists, a man with a fondness for expersive cars and fine cigars, was mourning the loss of Califano this past week over a lunch in a downtown Washington restaurant-Burger King. He is a lobbyist for the hospital industry and he has been fighting Califano over the Carter administration hospital cost containment bill (with considerable success) for 2 1/2 years.

His view is that Califano was so abrasive on Capitol Hill that the HEW secretary helped the lobbyist solidify votes against the Carter bill-which is now what the Carter White House is contending. Suddenly, the anti-Califano hospital man finds himself in league with the neo-anti-Califano president. And so a thought crosses the lobbyist's mind. In mid-Whopper, he asks:

"What can I do to get him to keep Califano?"