The nearly 3 million federal and military retirees who have been denied a 3.1 percent cost-of-living raise next month are the first and biggest group to feel the bite of the new balanced budget law.

The Gramm-Rudman- Hollings Act requires the government to balance the budget by 1991 by cutting federal spending by $36 billion a year. Many programs such as Social Security are exempt from the cuts, and trims are being made in federal-military payroll costs, pensions, insurance and other spending.

More than a dozen groups and individuals are planning to challenge various aspects of the new law. Among them:

*The National Association of Retired Federal Employees has filed in U.S. District Court here asking that the retiree cost-of-living adjustment be restored. The association contends that Congress acted illegally in canceling the COLA on Dec. 12.

The increase would have added about $30 a month to the pension check of the typical federal retiree here -- who now gets about $12,000 a year -- and about $14 a month more for the typical widow or widower of a government retiree.

*Rep. Mike Synar (D-Okla.) has also filed suit in the court challenging the trigger mechanism of the new law. It allows the Office of Management and Budget, Congressional Budget Office and General Accounting Office to decide how much government spending must be cut, and where those cuts will come from. He contends this is an end-run around the constitutional delegation of powers given to Congress and the president.

Most Washington area legislators voted against the Gramm-Rudman-Hollings Act. Those opposing it included Maryland Sens. Charles McC. Mathias Jr. (R) and Paul Sarbanes (D), and Maryland House members Michael Barnes (D), Steny Hoyer (D), Barbara Mikulski (D), Parren J. Mitchell (D), Helen Bentley (R) and Marjorie Holt (R), and Virginia Republican Reps. Stan Parris and Frank Wolf.

Those voting for the Gramm-Rudman-Hollings Act included Virginia Republican Sens. Paul Trible and John Warner and Maryland Rep. Beverly Byron (D). Meetings

The Arlington chapter of the National Association of Retired Federal Employees meets at 1 p.m. Jan. 8 at the Culpepper Gardens Recreation Center. Call 528-1020. People

The Senate last week unanimously confirmed Ralph E. Kennickell Jr. to be Public Printer. Kennickell, 40, has been head of the Government Printing Office since last December, when he was given a recess appointment by President Reagan . . . . The Senate also has confirmed Jerry L. Calhoun as chairman of the Federal Labor Relations Authority. Calhoun comes from the Defense Department, where he was principal deputy assistant secretary for manpower, installations and logistics. Christmas Eve Hours

The Office of Personnel Management says there will not (repeat, not) be a Christmas Eve, government-wide early dismissal of employes this afternoon. Some agencies say that between a fourth and half of their staffs are taking time off this week. But for those who remain on the job, it will be quitting time as usual today -- unless your immediate boss is touched by the Christmas spirit. Jobs

Defense has an opening at the Pentagon for a GM (merit pay) 14 personnel management specialist. Call Lisa Niesz at 697-8304.

The Army in Falls Church wants an employe development assistant, GS 5/6, and secretaries (steno and typing), GS 4/5 and clerk-typists, GS 2 through 4. Call 756-2006.