Because of the new budget crunch, the federal agency set up to protect whistle blowers and hear appeals of workers who believe they have been improperly demoted or dismissed may have to fire one-third of its own staff or close down operations temporarily early next year.

The Merit Systems Protection Board is one of many operations under orders to cut spending 16 percent between now and next September. The cut order came from the continuing resolution Congress passed Friday. It requires some government operations -- ranging from the General Services Administration to the White House -- to cut spending by the 12 percent President Reagan proposed earlier, plus another 4 percent carried in the resolution.

Labor-intensive federal operations -- outfits that spend most of their money on staff -- will be hardest hit. They have fewer programs to cut and must make dollar reductions by firing or furloughing people, or both. Some agencies now anticipate personnel cutbacks of 25 percent or more to meet the 16 percent spending reduction.

A number of departments and agencies are considering furloughs next year unless they get some kind of relief from Congress or the Office of Management and Budget. (Congress is hoping to recess today for the long Christmas-to-New Year's holiday.) Some departments (like Labor) hope to take money from low-priority programs to put into their salaries and expenses accounts to minimize the impact of RIFs or furloughs. Everybody -- budget officers, personnel officials and administrators -- is confused. That is the main reason there are so many wild (and some not so wild) rumors about RIFs and furloughs.

The small, 340-worker MSPB may have to RIF as many as 100 staffers next year. It is also considering furloughs, meaning a slowdown in processing already-backlogged cases from workers who allege they were fired or demoted without proper procedures, or as punishment because they had personality conflicts with the boss or because they embarrassed their political masters by pointing out (as the Reagan administration has asked them to) instances of waste, fraud or stupidity.

In the first two months of this fiscal year, MSPB has received 843 appeals from RIFfed federal workers; it got 800 cases in the preceding 12-month period. It is also scheduled to hear the appeals of 11,000 fired air traffic controllers, plus its regular number of appeals on demotions and from employes who have been denied disability retirements.