Ten days ago, Secretary of State Alexander M. Haig Jr. invited President Reagan's close friend, Sen. Paul Laxalt (R-Nev.), up to his 8th floor private dining room for a bit of informal lunching and back channel message-passing.

He wants very much to be a "team player," Haig told Laxalt, according to an informed source. He knows that he hurt himself badly with his early grabs for turf. He knows that he has this reputation now, inside the Reagan administration's highest councils, of not being a team player. But he wants very much to be one.

And -- most of all -- he wants to make sure the president gets this message.

There is a perception now among those close to Reagan and those close to Haig that, perhaps things are finally just a bit better for this secretary of state who had tried to begin as a ball-of-fire but who brought himself to the brink of self-immolation, instead.

But just a couple of weeks ago, many of these highly placed people were not sure that Haig would survive in the administration long enough to secure tenure, much less turf. And they caution that another outbreak of internecine warfare could mean Haig's swift updoing.

"There has been a lot of settling in in the last couple of weeks," said one senior administration official who is close to both Haig and Reagan. "If not, Haig could have been gone."

"Ronald Reagan had the ability to move very quickly when there's a problem that just isn't being resolved," this senior official observed."There is no warning, no sermon. But he can act very quickly. The case of John Sears is an example [Reagan summarily fired Sears as campaign manager last year when his differences with other Reaganauts proved irreconcilable.] Even Mike Deaver was once let go by Reagan, and it happened to Lyn Nofziger twice [both are now restored as Reagan advisers in the White House]. So it can happen."

For now, an uneasy peaceful coexistence has settled in, after almost three months of skirmishing that has variusly pitted Haig versus Defense Secretary Caspar W. Weinberger, Commerce Secretary Malcolm Baldrige, Special Trade Representative Bill Brock, and most of all, the senior officials of the Reagan White House, among them James A. Baker III, Edwin Meese III, Deaver and national security adviser Richard V. Allen.

Over at the White House, for the past three months, presidential advisers seethed over what they saw as repeated attempts to play "lone ranger" by the secretary of state -- efforts to seize policy-making machinery, crisis management machinery, and initiative in areas ranging from El Salvador to arms control, from East-West trade in general and auto imports in particular.

Haig called some meetings and took some policy actions on his own, as they saw it. He boycotted meetings that were convened by others in areas in which he wanted sole jurisdiction -- such as the time when Commerce Secretary Baldrige, acting under the designation of presidential counselor Meese, called a meeting on East-West trade policy.

They seethed in private at first, but in public eventually, raising their anonymous "White House officials" voices to complain that Haig was not acting in the president's best interests, but only to further his own.

Over at the State Department, meanwhile, the secretary and his intimates fumed as well, every time one of those anonymous quotes found its way into the public prints. They blamed the president's national security adviser, Allen, whose National Security Council staff has functioned at a low profile in this administration, as the source of many of these quotes.

They were rankled as well by presidential chief of staff Baker, whom they felt was among Haig's more vocal critics within. This fuming was fueled by the observations of Deputy Secretary of State William Clark, who entered office knowing little about foreign policy but much about Reagan. Clark has served as Reagan's first chief of staff in Sacramento, had originally hired Meese and Deaver onto the Reagan gubernatorial team and had worked with Weinburger more than a decade ago. In Washington, Clark has been forced to spend much of his time serving as Haig's personal ambassador to his own administration colleagues.

The deputy secretary of state is known to have reported to Haig that he felt Meese and Deaver were solidly supportive of him. He did not say the same for Baker.

Baker strongly maintained in an interview that, "It's not true that I'm leading the charge against Al Haig; it's a solid bum rap and I' don't think you'll find anyone who says I'm bad-mouthing Haig."

In fact, in the first 100 days of the Reagan administration, Haig seemed to be his own worst enemy. He did it to himself with his own stunning public testimonial of displeasure over a newspaper report that Reagan was placing Vice President Bush in charge of crisis management. And he did it again with his own unsteady public performance before television cameras when he explained how he was in control at the White House in the wake of the attempted assassination of the president.

All of this made Haig the subject of critical media attention at home, and perhaps most importantly, abroad. "We're seeing it in our daily foreign news digest in every edition," moaned a senior State Department official. "Those stories that say: 'Is he or isn't he?'"

And it was these public performances by Haig that made him the uncomfortably subject of nightly attention from one of America's most formidable molders of public opinion: The Johnny Carson monologue. Example: There is good news and bad news today. The good news is that President Reagan is coming home from the hospital. The bad news is that Alexander Haig has barricaded himself inside the Oval Office with a four year supply of Spam.

It was the day of the flap over the president's decision on crisis management, and when national security adviser Allen walked into the Oval Office, he found the president, the vice president, and advisers Baker, Meese and Deaver convulsed with laughter.

"What are you laughing at?" Allen asked, according to one who was present.

"You," came the reply.

Somebody then explained that in the deliberations over what to do about Haig's public testimony over Reagan's reported plan to put the vice president in charge of crisis management, somebody had asked where Allen stood on the matter. And somebody else had answered: "When the elephants start fighting, the monkeys go up the trees."

Allen joined in the laughter, but he paused long enough to add: "Yes, but in this case it's a 500-pound gorilla that's going to come down."

In the weeks, to come, Allen would take delight in telling the story to a number of people inside and outside the administration.

That was the day that the president and his advisers had decided to announce that the published report that had so angered Haig and had prompted him to express doubts about its authenticity, was in fact true -- that Bush would head crisis management. The secretary of state was not informed.

At 6:15 that evening, a reporter called State Department spokesman Williams Dyess to ask for Haig's reaction to the announcement that had just been made over at the White House. Dyess went to Haig and asked what he should say. Haig responded that the reporter was wrong, that there had been no suchy decision or announcement.

When Dyess relayed this to the reporter, he was told that, no, Haig was wrong, that the announcement had indeed been made. Dyess reported back to his boss; Haig telephoned White House press secretary James S. Brady. It was then, for the first time, State Department officials have been told, that Haig learned of the president's decision.

Later that evening, deeply distressed, Haig dictated a statement of resignation. But his deputy secretary, Clark, talked Haig out of delivering the letter to the president, after a lengthy conversation that lasted into the night.

This was a traumatic moment for the secretary of state, one that worried many of those who are close to him today and who have known him in the past. He has appeared a much more intense man than he was in his past Washington assignments, reacting with greater intensity and angering more easily than he used to in those days when he served as an aide to President Nixon's national security adviser Henry A. Kissinger, and even in those final days when he served as the chief of staff presiding over the last days of the Nixon presidency.

Haig has been through a lot in the years since: an assassination attempt on his life when he was the chief of the NATO command, and more recently, a triple-bypass open heart surgery. And this is a matter that has been discussed privately and sympathetically by those close to Haig and by those on the White House staff who are anxious to make the relationship between Haig and the rest of the Reagan administration work.

The concern over Haig has been a subject of internal discussion and controvery from the beginning, when he handed Meese on inauguration day that now-celebrated memo that amounted to his effort to design an administration foreign policy and decision-making apparatus with himself at the top. Haig's proposal prompted Weinberger to counter with a memo of his own. Which prompted Haig to pick up a phone and call the defense secretary.

"You're accusing me of trying to rape the department," Haig said with apparent anger in his voice, according to one source who reconstructed the exchange. When Weinberger said this was not so, Haig replied to the effect that he had a copy of Weinberger's memo in front of him and that it did indeed amount to an accusation of bureaucratic rape.

In fact, what upset Haig, according to an informed source, was that Weinberger had taken the listing of the duties of the secretary of state and secretary of defense that was contained in Haig's original memo and had added a few insertions -- all of them limits and caveats in the secretary of state's column.

Haig felt the insertions only to his side "produced a lack of parallelism," according to one source.

Soon after, the two men got together and agreed to agree. They produced a letter that was dated Feb. 5, but which did not arrive at the White House until later in the month. It said that "Cap and I have agreed to the following process" -- and then outlined a process of policy decision-making that became the basis of the agreement between the two men.

Relations between Haig and the rest of the administration have come down now to two basic points:

There is the view of Reagan's close advisers, who believe, as one of them said, "If Al makes the adjustment it can work."

And there is the view of Haig's State Department associates, who believe, as one of them said: "Haig's problem is not with the president but with the White House staff. The effort to improve things has to be made on both sides."

It was in this spirit that Haig broached the matter last Wednesday with President Reagan. Haig has no longstanding friendship with his boss, and when they meet privately, their discussion is almost always devoted solely to matters of substance, Haig's aides say. But last Wednesday, Haig diverted the discourse long enough to protest an anonymous quotation that had appeared in the New York Times the day before, attributed only to a senior White House official. It quoted the aide as saying that Haig had gotten "somewhat out in front" of Reagan by saying that if the Soviets invaded Poland, the United States would clamp an "across the board" embargo on all U.S.-Soviet trade.

In fact, Reagan shares this view -- it has been agreed to in a recent meeting, according to one presidential source. And State Department spokesman Dean Fischer also concedes that by virtue of the fact that Haig has become the first to state the total embargo threat, he has, by definition, gotten out in front of Reagan on it.

But Haig chose to use this episode as the vehicle to drive his point home to the president: the anonymous quotes from White House aides were undercutting him and administration policy.

Haig reported back to his department advisers that the president had been "totally supportive." The president, it appears, did not say anything to his staff.