Calling the Reagan administration's across-the-board budget cuts at the National Archives an "atrocity," Pulitizer prize-winning historian Barbara Tuchman told a House Government Operations subcommittee yesterday: "It's like the burning of the Library of Alexandria in the third century, B.C. The ancients wept at what was lost."

"Most of history will never be written," Alex Haley, author of the best-selling "Roots," echoed. "The next best thing we have is the Archives.

Similar concerns were raised by scholars, historians, genealogists and others who use the Archives. The reduced funds have forced staff reductions and cutbacks in cataloguing and research services.

The Archives' budget was cut by 16 percent for the current fiscal year. Since almost half the budget is for fixed costs, such as rent, heat and light, most of the 16 percent must come from the operational half. The result is that the payroll has been cut by almost 30 percent and the archivist staff by more than 20 percent, which drastically reduces the number of requests for records the Archives can fill and brings to a standstill the declassification and acquisition of records.

"This is of the most serious concern to the academic profession," Dr. Richard Leopold, professor emeritus of history at Northwestern University and chairman of the National Archives Advisory Council, said in a telephone interview. "It's going to have a paralyzing effect on the use of the Archives."

Scholars now must wait two hours to look at records kept by the diplomatic, judicial and fiscal branches, which hold the records of the State, Justice and Treasury departments. Telephone and mail requests for records are no longer honored if the material takes longer than 30 minutes to find. Xerox copies of records anywhere in the Archives are now limited to 25 per person. Previously, the only limiting factor was the charge per copy.

Fourteen of the 31 archivists handling President Nixon's tapes and papers have been laid off, including five cleared for top secret work. This means the Archives can't hope to meet its 1985 deadline for clearing the Nixon tapes for public listening; so far, 12 1/2 of the 4,000 hours of tapes have been cleared. It also means the Archives won't meet its 1985 deadline for clearing Nixon's papers. Out of 40 million pages of papers, none has been released.

The orders for computers that were to process about 1,200 other tapes have been canceled. Among the tapes are the Pentagon's records of the United States' involvement in Vietnam.

Under serious discussion is a $2 admission fee, $5 for an answer by mail and a $7.50-per-hour fee for research of any kind. Also under discussion are nighttime and weekend closings. Currently, the Archives is open at night and Saturdays for researchers who can't work there during regular business hours.

Another proposal is to give each of the remaining archivists 22 days of unpaid leave from April through October, staggering the furloughs so everyone isn't off at once. It works out to a four-day week during the time when scholars and historians are on leave and making their greatest demands on the Archives' staff.

What archivists call the "accessioning" of new records has come to a halt. Public release of the FBI's records of the J. Edgar Hoover years, the Justice Department's World War II files, the Pentagon's and State Department's central files of the Korean War years--all promised for this year-- has been delayed indefinitely.

"If Reagan breaks up the Department of Energy as he says he wants to, we may never know how energy policy was being formulated in its early years," said Anna Nelson, professor of history at George Washington University and a former staff member of the Public Documents Commission. "When you cut back on the number of archivists, you cut back our understanding of contemporary history."

Behind the scenes is a fight between the Archives and its parent organization, the General Services Administration. Archivists insist the firing of 30 percent of the staff will save the government no more than $1 million annually in salaries. They are lobbying on Capitol Hill to restore Reagan's budget cuts and for legislation to make the Archives an independent agency. More than half the 14 witnesses who testified before the House Government Operations subcommittee yesterday called for severing the Archives' connection to GSA.

"Independence would remove the preservation of documents process from political manipulation," Dr. Joan Hoff-Wilson, executive secretary of the Organization of American Historians, told the subcommittee. "It would allow the Archives to build a constituency throughout the country, which it so badly needs and deserves."

GSA officials counter that the Archives has acted too independently, too long.

"The National Archives lacks good management," GSA Administrator Gerald P. Carmen told the House Appropriations Committee earlier this month, "because it is run by historians and scholars rather than managers."