The White House has a tough time keeping its temperature at 68 degrees. Like presidential popularity polls, it goes up and down.

Over at the Department of Housing and Urban Development, some workers on lower floors claim it is so cold they can see their breath.

At the General Services Administration - the housekeeping arm of government that controls thermostats - it got so hot this month that top officials had to demand that the heat beturned off. And so goes the Carter Administration's relentless (some claim unwinnable) war against eneryy waste in the government's 250 Washington area buildings of all sizes, shapes, styles and ages, around the nation.

At one suburban Army building, workers have been told that the policy of the government is to keep the building at 66 degrees. The White House says it is trying for 68 degrees.

According to reports, and very unscientific measurements by this column over a one-week span, the temperature range in government offices was from 54 degrees to 81 degrees on the same day. As Mark Twain might have said, "Everybody talks about the weather in government but nobody can do anything about it."

Officially, government offices are told to shoot for a temperature range of between 65 and 68 degrees. People being people, that is a happy condition for some and sheer misery for others.

"It's one thing to set an energy policy for government offices," said one top government manager yesterday, "and it's another thing to make it work. Really all we can do is try."

Many of the town's 347,000 federal workers are burning up, freezing or confused because of the energy policy. That is because, for all its simplicity, it is a confusing policy.

Getting most parts of a big building to the 65-to-68 range is difficult. Getting all parts of some buildings to that White House-mandated range is virtually impossible.

An official in charge of the temperatures in his building sums it up: "This place was put up about the end of World War I. When the sun comes into my window in the morning, we burn up. In the afternoon I freeze . . . There are some offices in this building where the temperature never hits 65 in the winter."

Complaints about cold, clammy conditions often can be taken care of, officials say, by cranking up the furnaces for a time. The problem is offices where it is too hot, even when it is freezing outside.

According to government policy, no energy can be expanded to lower indoor temperatures in winter. That means they can't (or aren't supposed to) turn on the air-conditioners in winter. "You can open a window, or we can turn down the heat," a building manager said. "But if you don't have a window, you are out of luck."

The same holds true for people who shiver in the summer when the outside temperature is 99 and the indoor readings are in the 50s. No energy can be expended then to raise the temperature. They, too, have to depend on opening windows. The problem is that most of the new government buildings have sealed windows, so people who are cold in winter bring in space heaters, which of course use energy.