As the Office of Management and Budget announced budget cuts mandated by the Gramm-Rudman-Hollings deficit reduction law, federal agencies yesterday began figuring out the impact on their staffs and programs.

Federal workers immediately began to think of layoffs, freezes and furloughs.

But Office of Personnel Management Director Constance Horner said the government has "learned a lot about how to cope" with tight budgets since it underwent disruptive, morale-bruising layoffs several years ago.

Horner, who was with OMB before becoming the government's personnel czar, said, "We ought not to succumb to panic induced by telling each other panic stories . . . there are a broad range of options, so we can select the most humane and effective ways to meet the budget requirements."

OMB and GAO yesterday made official what most agencies have known since Friday: civilian departments must cut their budgets 4.3 percent (with Defense taking a 4.9 percent cut) during the seven months left in this fiscal year. Those cuts are required to comply with the complex, untested new law, which is already the subject of political battles and court cases.

The new act requires agencies to cut spending between now and 1991 to balance the budget. That means a cut of $11.7 billion from current agency budgets between now and September. Budget and personel officials agree it could be months before the full impact of the cuts is clear.

Some agencies, in anticipation of the cuts, have already drawn up plans to furlough workers or freeze hiring and promotions.

The National Treasury Employees Union -- which represents 227,000 workers in Treasury and Health and Human Services plus other agencies -- said the cuts could trim as many as 16,000 jobs in the two departments.

However, Thomas S. McFee, assistant secretary for personnel administration at HHS, said the department has no plans to lay off any of its 102,000 workers. He said NTEU's assessment is "way off base" and that the worst-case scenario is that some HHS units might have to furlough employes one day every two weeks. Hiring, most travel and overtime have been frozen, he said.

An Agriculture Department official said the agency hopes to use early retirement authority and other options to avoid layoffs of 109,000.

The manner of effecting the cuts will vary between departments and even within agencies. Portions of some agencies may not feel the blow.

The Veterans Administration, for example, has 220,000 employes and one of the biggest budgets in government. But 194,000 VA workers are directly involved in medical care or benefit payments to veterans, programs that Congress has exempted from cuts.

Horner said department heads will decide how to make cuts, but OPM will stress the implications -- in cost and in humanitarian terms -- of furloughs versus layoffs, and of options such as allowing workers to take early retirement (at age 50 with 20 years' service) to protect younger workers' jobs.

During the first three years of the Reagan administration federal agencies fired more than 12,000 employes -- including about 3,000 here -- for economy reasons. Government studies later showed that layoffs are often the most costly way to reduce employment. The layoffs produced tragicomic results in some agencies: employes were fired only to be rehired as consultants, and highly paid scientific and medical specialists were dropped -- at the same salary -- to low-paying clerical jobs.