When President Carter flew to South America and Africa to help solve Third World problems, the stay-at-home White House staff broke out the mousetraps and poison pellets.

During the critical coal strike negotiations, Labor Department aides carefully concealed mouse-catching devices behind heavy curtains so that union aides would not spot them.

Before a recent meeting with regiona officials at Housing and Urban Development, departmental employes attempted to seal off rooms so that the tiny rodents would not make unannounced visits and disrupt the heavy talks.

All this leads up to the fact that the world's most powerful government - with its military, political and moral clout - can't shake mice who have nested throughout the federal establishment.

The problem is that mice do not respond to jaw-boning or threats of federal takeovers, and have no fear of losing government subsidies for food or housing. They are everywhere in government, from the Pentagon to the State Department and all points in between.

THe mouse situation has become so bad in some agencies that some Gmen and women bring their own mousetraps to work each day, and run to them each morning to see what surprises they may hold.

Mice reportedly have popped out of desks in the Patrick Henry Building, scuttled down the halls of the U.S. Postal Service's plush L'Enfant Plaza Building, and nibbled wires leading to exhibits at the Smithsonian Institution.

Federal officials believe they will have solved the problems fo inflation and perhaps even have brought the Middle East to a lasting peace before the mouse situation is brought to a close.

The White House problem is made even more difficult because it is an old building, surrounded by grass and trees, and serves both as an office and a residence for the first family. Mouse-catchers at the executive mansion are loathe to spray, bait or trap the rodents when the president or his family is around, which is most of the time. They welcome overseas visits as a chance to get on with the never-ending job of rodent control.

Labor Department officials broke some of the recent coal-bargaining tensions with mouse jokes. Great pains were taken so that television cameras covering the sessions didn't pick up that embarrassing secret.

In an April 4 speech on collective bargaining in Atlanta, Labor Undersecretary Robert J. Brown let the cat out of the bag. He confessed that mice were plaguing the department. He said it just goes to show that even Secretary Ray Marshall, with all the powers vested in him, can't make a settlement with the mice.

"The problem," a federal rodent fighter said, "really isn't funny. We get lots of complaints about mice. The metro construction uprooted them, and food left by Metro workers nourished the mice."

He noted that many federal workers brown bag it to work, and leftover lunches have shown the mice something others have known for a long time: that the govenment will provide.

"Mice, as you know, are romantic creatures. They produce from four to seven young every month, like clockwork. That is one population explosion problem very close to home," he said.

One official pointed out that recent presidents have all been dog fanciers. "If we could get a cat man into the White House," he said, "maybe that would do it."

Richard Galleher, research director for AFL-CIO's Public Employes Department, will be in Doctors Hospital through next week for tests. Galleher, 34, suffered chest pains Wednesday evening after leaving a meeting among White Hous aides and the Federal Employes Pay Council. Galleher has been chief spokesman for the unions in opposing any mandatory pay controls for federal and military personnel.