The Treasury Department's Bureau of Alcohol, Tobacco and Firearms--enforcer of the nation's firearms, explosives and arson laws--may be forced to furlough nearly two-thirds of its employes without pay for three months because of budget problems.

The agency has long been a target of the powerful National Rifle Association and other champions of the right to freely carry firearms. It has been operating under a cloud of uncertainty since President Reagan announced last year that he planned to carry out his campaign pledge to abolish BATF.

The administration has announced plans to transfer BATF's personnel functions to the Secret Service and the U.S. Customs Service, other agencies within the Treasury Department. But the NRA has strenuously opposed that plan, fearing that the Secret Service might be even more vigorous in its enforcement of the gun laws. Congress is still arguing with the administration over exactly what will happen to the agency.

As the controversy has continued, the BATF budget has been severely reduced--from $150 million last year to $112 million this year. The agency had asked Congress for a supplemental appropriation of $26 million to finish out the year, but that amount already has been cut by the House Appropriations Committee to about $15 million and could be eliminated when it comes up on the House floor, probably next week.

BATF agents say that because of the money shortage, the agency has already cut back to about half its regular level of investigations and has severely reduced funding for travel, paying informers and making undercover street buys.

In Florida, for example, agents say that in the first 12 days of this month, they used up their per diem travel money for the next three months. That means that through the end of June there will be no out-of-town criminal surveillance by BATF in a part of the country noted for its shipments of explosives and silencer-equipped machine guns.

If the furlough goes through, one BATF official said, "it would basically rape the organization. It would wipe us out. It would blow us away. We'd be a skeleton crew with no resources."

Two internal memoranda written last week by BATF Director G. R. Dickerson indicated that if the supplemental appropriation is not approved, 1,600 of the agency's 2,700 employes will have to be furloughed without pay from June 27 until the new fiscal year begins on Oct. 1. Dickerson refused to comment on the memos, which were obtained by The Washington Post.

BATF, which also enforces regulations and collects taxes involving the alcohol and tobacco industries, is already operating at well below its authorized staffing level.

Because of the confusion and uncertainty about the future of the agency, the number of personnel has dropped sharply. More than 1,000 employes have left in the past year, including more than 700 since the start of the fiscal year last October. In fact, even Dickerson has resigned--effective last Friday--to go to Customs as deputy commissioner for international affairs.

Dickerson's memo, addressed to John M. Walker Jr., assistant secretary of treasury for enforcement and operations, warned that if the supplemental appropriation is not approved, "most furloughed employes may never return to the bureau given the length of the furlough period."

In the memo Dickerson said that to operate even at the sharply reduced levels, the agency has been spending more than its allotted budget amount for the past six months. "Our only really viable plan of action at this time is to shut the bureau down, except the essential functions tax collections and emergency law enforcement when the money runs out," the memo said.

Meanwhile, agents say they're having a hard time concentrating on their work as they wait for the ax to fall.

"It's as if we're dead already," said one agent. "Gun dealers are calling up all the time asking when they're going to be able to stop keeping their gun sales records. . . . It's hard to get out there and do anything when you don't know for sure whether you'll be fired by the time you get back to the office."

Many employes are frantically searching for new jobs. One BATF employe who recently left said he felt "guilty" leaving the organization when it is in such bad shape. But he said, "I just couldn't stand it any more. It made me sick to watch it dying."