March 29, 1981

About 11 P.M. Tuesday, after a long, bruising day of trench warfare with Secretary of State Alexander M. Haig Jr., the White House was uncertain whether he would resign. Dave Gergen, a top White House official, telephoned William Dyess, an aide to Mr. Haig, to ask: ''Is he or isn't he?'' It was a pivotal moment in a bureaucratic battle that almost turned the first-ranking member of the Reagan Cabinet into its first political fatality, the victim partly of his own urge to take full command in an Administration where the President reserves that power to himself and expects from his Cabinet the collegial give-and-take of team play. The showdown was over power and prerogatives rather than over policies. Mr. Haig shares Mr. Reagan's broad foreign policy objectives. But his confrontational assertiveness rubbed against the more relaxed style of the President, who apparently had promised his Secretary of State more authority than he really wanted to surrender to any one man, and then shied away from curbing Mr. Haig until he himself felt challenged.

Phil Mahre of Yakima, Wash., today became the first American to win the World Cup, which has been awarded the last 15 years to the skier who accumulates the most points from 31 downhill, slalom and giant slalom races. The series is held over a four-month span in 10 countries. By finishing second in the giant slalom here today, behind Aleksandr Zhirov of the Soviet Union, Mahre earned 9 points, enough to pass Ingemar Stenmark of Sweden, who won the trophy in 1976, 1977 and 1978. Stenmark was leading the overall standing before today's final event.

ACONTROVERSIAL Army Corps of Engineers proposal to bury the 15 existing rock groins in Westhampton Beach - jetties built by the corps to prevent coastal erosion but not believed to accelerate it in adjacent areas - has been blocked by Suffolk County's refusal to approve the $42 million project. County Executive Peter F. Cohalan said he would not approve Suffolk's 9 percent share of the cost because ''the people who would be paying for it would derive little or no'' benefit from the project. By Federal law, all projects undertaken by the Corps of Engineers must be approved by the state and county involved. In addition, the state is required to pay 21 percent of the local cost and the county 9 percent; the remaining 70 percent is paid by the Federal Government.

JAMES L. EMERY, who succeeded Perry B. Duryea of Montauk as the Assembly minority leader and would like to succeed him as a Republican gubernatorial candidate against Governor Carey, has established a political foothold on the Island, the home turf of another G.O.P. gubernatorial prospect, Court of Appeals Judge Sol Wachtler. Mr. Emery has dispensed considerable patronage to the Suffolk Republican organization, a move that could prove to be a counter to the solid Nassau Republican organization support of Judge Wachtler, a Great Neck resident. Mr. Emery, a Geneseo Republican, has named the Conservative Party's county chairman, Neil A. Greene; the Babylon Town Conservative leader, Pasquale Curcio, and the Smithtown Republican chairman, Frank Apollaro, to what Republicans describe as ''seldom show'' jobs in his regional office at the State Office Building in Hauppauge. The two Conservatives are paid $9,300 each annually, while Mr. Apollaro's salary is $15,938. Other Republicans on the Emery payroll in Suffolk are Barbara Labrador, who heads the Suffolk office and is paid $20,280 annually; Diana McKenna, a secretary, $10,036, and Thomas Neppell, the former Brookhaven G.O.P. leader, who is being kept on the payroll for state fringe benefits, $2,470. John Galla, a holdover from the Duryea era, who was paid $17,940, left the Emery staff last month.

The Reagan Administration is planning major changes in the way national parks are operated, including granting increasing power in running the parks to private concessionaires and possibly divesting the system of urban parks such as the Gateway National Recreation Area in the New York metropolitan region. President Reagan's budget would eliminate all funds for the acquisition of new park lands that have been authorized by Congress. But the Department of the Interior, under Secretary James G. Watt, is planning other far-reaching policy decisions on how the parks are operated and how the system is administered. To turn the urban parks over to state or local government, or to drop parts of other parks through sales or land swaps, which is also a possibility, the Park Service would have to ask Congress for enabling legislation. Such an effort almost certainly would be opposed on Capitol Hill by environmental groups and probably by municipalities that do not want the task of operating the parks.