Last year, Congress with great fanfare passed an omnibus bill to fight drug trafficking, and as part of it the Coast Guard was given a massive infusion of planes, helicopters, boats and radar equipment to help expand coastal patrols for drug-laden ships and aircraft.

But with the Coast Guard still awaiting delivery on some of the new equipment, the agency is facing budget cuts on Capitol Hill that could dampen its new antidrug mission and require cuts in its traditional role in boating safety and search-and-rescue activities.

The problem, according to sources in the administration and on Capitol Hill, is that the Coast Guard is funded in the Transportation Department budget, and the House Appropriations transportation subcommittee decided to cut $150 million from the Coast Guard to help restore funding the administration had tried to cut from Amtrak, highway construction and big city mass transit projects.

One source complained that the members, backed by the full House when it approved the bill July 13, decided to protect "pork-barrel projects" while cutting programs dealing with law enforcement and public safety. Despite the cuts, the total transportation budget is $3.3 billion higher than the one requested by President Reagan.

But other congressional sources said committee members feel that if the Coast Guard has a problem, the money is sure to be restored in a supplemental budget later in the year. The Senate Appropriations Committee also may make changes in the bill.

In addition to the Coast Guard cuts, the House cut out 4.6 percent of the budget for the Transportation Department's inspector general, $65 million from the Federal Aviation Administration's operations budget and another $200 million from the FAA's facilities and equipment appropriation.

According to Adm. Paul A. Yost Jr., Coast Guard commandant, the fiscal 1987 Coast Guard budget was $2.913 billion, including a one-time $128 million appropriation related to the new drug enforcement program and $275 million transferred from the Defense Department budget.

Reagan has proposed a total Coast Guard budget for fiscal 1988 of $2.734 billion, which Yost said in an interview he can "live with," even though he considers it "austere." But the House budget, passed July 13, cut another $150 million from the Coast Guard, which means "I've got to decommission something," Yost said.

Yost refused to say exactly what he would cut. But the Coast Guard has said it could save about $100 million by closing six of the 28 Coast Guard air stations, 17 of the 176 search-and-rescue stations and taking out of service 30 of the agency's 166 boats and five of its 68 aircraft. The agency has estimated it would have to cut about 2,500 positions to save $118 million.

The House bill directed Yost not to cut the Coast Guard's role in drug enforcement.

The Coast Guard has never been a heavily funded agency, and it has not fared substantially better under the Reagan administration. Even with increased funding and added personnel in the last couple of years related to drug enforcement responsibilities, the agency has nearly 1,000 fewer employes than the 39,450 it had in 1981.

The current House cuts have caused a flurry of protest.

Attorney General Edwin Meese III wrote to Senate Majority Leader Robert C. Byrd (D-W.Va.) on Sept. 17 saying, "A $150 million reduction in a budget that is 70 percent operating expenses would have a devastating effect upon the Coast Guard's ability to reduce the flow of drugs into this country." He added that "stripping resources from a major participant in the drug control program . . . threatens this national commitment."

Rep. Earl Hutto (D-Fla.), chairman of the Coast Guard subcommittee of the Merchant Marine and Fisheries Committee, has sent around a "Dear Colleague" letter expressing his concern.

In an interview, Hutto said, "It's crazy. I'm really concerned . . . . We continue to mandate new missions for the Coast Guard: drug enforcement, search and rescue. We buy them sophisticated equipment. But then we don't allow them to have the people and the wherewithal to operate this equipment.

"The Appropriations Committee really gave them a lick. {The Coast Guard} has to compete with so many other things like Amtrak and mass transit. They just didn't put the proper priority on the Coast Guard, and I'm not optimistic it will be fixed as much as it ought to be."

House staff sources familiar with the deliberations on the Coast Guard appropriation say that the cuts were made with the understanding that an extra $100 million would be given to the Coast Guard out of the Defense Department budget.

Rep. William Lehman (D-Fla.), chairman of the Appropriations transportation subcommittee, said: "Based on historic precedent, we were expecting $100 million from the defense budget. Our subcommittee wouldn't do anything to hurt the Coast Guard. I think they're going to be all right."

But the money isn't reflected in the Reagan Defense Department budget, and the House Appropriations subcommittee that deals with defense spending has not agreed to the arrangement.

The Appropriations transportation subcommittee initially planned to cut another $175 million from the Coast Guard budget on the assumption it could come out of the defense budget, but that amount was restored to the transportation budget after Rep. Bill Chappell Jr. (D-Fla.), who heads the defense subcommittee, made it clear that the defense budget could not accommodate the Coast Guard.

Hutto wrote to Chappell on Sept. 14 asking him again to try to come up with $100 million from the defense bill, but it is not clear what the subcommittee will do.

"I'm not optimistic that it will be fixed as much as it ought to be," he said, adding that it would make more sense to move the Coast Guard to another budget category and stop funding it out of the transportation budget where it faces much competition from discretionary projects. "I just don't think they ought to be competing against mass transit," he said.

Yost agreed: "As long as the Coast Guard is under the {transportation budget}, where it {has} to compete with grant programs . . . it's like being in the ring with Joe Louis every year. I know I'm going to get hurt. I just don't know how much."