Not even the personal insults being hurled between the White House and Foggy Bottom by close aides of Ronald Reagan and Alexander Haig reveal the measure of the secretary of state's defeat at the hands of the White House and its high-riding chief of staff James A. Baker III.

Haig's humiliation was embellished the evening of March 24 by how he first got word that the White House staff had persuaded Reagan to put Vice President George Bush in charge of national security crises. He learned it by a wire service ticker shory handed to him as he was ending a half-hour visit from British Ambassador Nicholas Henderson.

By not immediately resigning, a step he has threatened repeatedly since Jan. 20 but never directly to the president, Haig accepted a public rebuke. That weakens his prestige abroad, his power in the bureaucratic wars here and his self-esteem. This potentially costly impairment of the secretary of state bodes ill for the Reagan administration in the future, despite frantic efforts to paper over the grievances.

Haig's problems with the White House dte to Inauguration Day, when he tried to gather all foreign policy-making in his hands. Baker and presidential counselor Edwin Meese III stepped in to block that move, setting off an increasingly bitter struggle based on personality and power, not issues and ideology. By the sad events or March 24, the president's senior aides seemed not to care how much they damaged the secretary of state, so eager were they to put him in his place.

Relations between Haig and the White House staff, particularly Baker, have been deteriorating for weeks. Haig, who had considered himself Reagan's foreign policy "yicar," resented statements and backgrounders by national security assistant Richard V. Allen and his subordinates, particularly Dr. Richard Pipes. Haig assistants at the State Department attacked the White House staff as "a mandarin's court." Haig himself complained to one aide that Reagan alone "is worth 10 times those staff people."

From the other side, the shafts were sharper: questions about Haig's health, his "temper tantrums" and his insistence on aggrandizing his power. Haig moved early the week of March 16, a week before he knew about the elevation of Bush, to establish regular, direct access to the president three days a week without "those staff people" monitoring him. His model was John Foster Dulles, President Eisenhower's secretary of state. On national security, Eisenhower listened only to Dulles.

The first of the three-a-week Oval Office tete-a-tetes was March 23. Only the day before Haig had first learned that Bush was in the picture as a possible national security crisis manager (although it was first reported on March 6). Wholly unaware, Haig was therefore incredulous when he read the page on headline in the March 22 Washington Post: "Bush to Run Crisis Management." So, Haig immediately counterattacked the morning of March 23 in Reagan's office.

Haig might have sold the Ike-Dulles model to Reagan if it were not for Baker and Allen. They had been converted by Haig into caustic critics. Allen also resented Haig's unnoticing treatment of him. Elsewhere in the White House, Meese was alarmed by Haig's quest for power and Bush was eager for a place in the sun.

Not waiting to give Haig the chance to convert Reagan, the Bush arrangement had been settled with the president by Baker, Meese and Allen. That was the situation when Haig was asked about it in testimony before the House Foreign Affairs Committee on March 24. His public criticism of the proposal galvanized Baker and Alklen, who persuaded Reagan to issue the order that very day and stymie Haig's counterattack.

"If he quite, let him," one presidential staff said. "Better now than later." That does not reflect today's mood of Reagan's senior advisers and certainly not of Reagan himself, but it suggests the change in the White House.

This holds an ominous portent for Reagan's foreign policy, which is now to be conducted more by committee than Haig ever bargained for when he accepted his post. The victory of Baker and the White House staff over the man thought to be the Cabinet's most powerful member is another suggestion that Cabinet government is an illusion.

For Haig, friends are saying it's only the loss of an early skirmish. Haig knows better. He was learned the hard way that taking on the president's men is a losing war in which he has turned up on the first casualty report.