Government Printing Office, one of the world's largest print shops and one of the biggest federal operations here, will furlough about half of its 6,300 staffers for 12 days starting in mid-May.

GPO, which is supposed to break even, has been losing about $1 million a month over the past five months in its printing and binding business. Because of the dramatic loss and a decline in work orders, it will rescind an average 16 percent price increase it ordered early this month.

Cutbacks in funds and publications at other federal agencies have reduced their printing work, and GPO -- part of the legislative branch -- is having money problems.

Public Printer Danford L. Sawyer Jr., the Florida businessman brought in by the Reagan administration to run GPO like a business, said he will return five percent of his $58,500 salary to the Treasury as long as staffers are on furlough.

The furloughs will cover about half the GPO work force, including craft and white collar personnel. Those exempt from the furloughs -- which will be one day every other week for six months -- include some production, security and management people. The furloughs also will hit facilities in Seattle, New York and Denver, but not the Chicago office.

Sawyer, who advised GPO unions of the furlough late yesterday, said the choice was between furloughs and layoffs. He also said GPO hopes to further reduce prices charged for publications in months ahead.

He wants to hire an outside consultant to study GPO operations and make cost comparisions between doing work in-house, and contracting it out to the private sector. Much of GPO's work already is contracted out. Metro Washington area firms get about $5 million of that business yearly.

A number of federal agencies, facing money problems, either are furloughing workers or plan to do so. More than 3,000 Census Bureau workers started furloughs, one day every two weeks, earlier this month. The Office of Personnel Management has announced it will have furloughs, in addition to layoffs already completed. General Services Administration, parts of the Treasury Department and other agencies are also considering furloughs.

Federal Aviation Administration (with 2,000 workers here) temporarily has postponed furloughs due to begin in April for 30,000 workers nationwide. FAA originally planned to furlough employes for 12 days, but now hopes it can limit the furloughs to six days or less.