THE PRESIDENTS ALWAYS live in another Washington -- not that of the tourists, not that of the locals.

Jimmy Carter occasionally dropped in to visit the real D.C., but his Washington, outside official circles, was the Kennedy Center, the National Theater, Paul Young's Restaurant and Rosalynn at D.C. General.

Ronald Reagan has been here a couple of months and his idea of Washington is the Marine Band playing at a dinner of the Alfalfa Club, trumpets sounding in the Rose Garden. He doesn't do the District of Columbia, the real city. And now it is apparent he doesn't even see the Washington of the tourists. If he did, there is no way he'd let his budget cutters deep-six the National Aquarium.

Now granted, the aquarium is not the Las Vegas of museums. Even as tourist and schoolchildren attractions go, it is not big fish. The 500,000 people who visit it each year don't compare with the 3.5 million who go to the zoo or the 7.2 million who troop into the Air and Space Museum.

But the kids like it. When I dropped in the other day, Ted Hendricks, 11, was saying they only had a "real small" aquarium in Lilburn, Ga., and he'd be hard-pressed to "explain the beauty" to anybody who hadn't seen it first hand. Bill Rose, 13, of Clovis, N.M., was getting an eyeful of "all I'd missed growing up on the desert." And Rick Terry, 16, was thinking of the future cultural deprivation of his 9-year-old brother back home in Lanett, Ala. "I think he ought to get a chance to see it. He loves fish."

I could understand eliminating it if the aquarium was some idealistic, new-fangled, throw-money-at-the-problems program instead of 108 years old and part of the cultural history of this country.

I could understand eliminating this museum if it cost a lot of money instead of only $280,000 a year.

I could really understand cutting spending at the National Aquarium if it was like the Defense Department budget.

For while they're putting the aquarium out of business, the Reaganites are making Defense a sacred cow and slating it for enormous increases even though the General Accounting Office, for instance, has pointed out that mismanagement and waste are now adding "several billion dollars a year" to the Pentagon budget.

I could understand eliminating the aquarium if it cost the $376 million a year the Defense Department spends providing certain repairs and supplies to the Army, Navy, Air Force and Marines in geographic areas where each has a base and offers the identical services.

I could understand eliminating the aquarium if it cost as much as the XM1 supertank -- $2.5 million per tank, and nobody still is sure if it's worth it.

But while they're putting the aquarium out of business, the Reaganites are putting two ancient battleships, the Iowa and the New Jersey, into business at a cost of close to a billion dollars. They don't even have enough petty officers to man all the ships that are now in service.

I could understand if the Reagan budget-cutters had put the question to the people who cared about such things as aquariums and they at least had a fair hearing. But they didn't, and i can understand why people, such as Wayne Hilburn, a member of the Potomac Valley Aquarium Society, are boiling.

"Their idea is don't raise a public outcry," he told me indignantly, and sounding for all the world like a man who voted for Reagan. "To me, public outcry means people have something to say.

"I don't know who the people were who had to stand up in 1930 and say we support a first class National Aquarium in D.C., but now I feel it's time for some of us to stand up. I don't think you have to believe that Mr. Reagan was elected to office for the express purpose of shutting down the National Aquarium."

Wait, Mr. Hilburn. I can understand not. I think I've got it figured out.

The aquarium was swallowed up precisely because it was such small fish. It's the little fish the Reaganites like to go after -- little fish on welfare and Medicad and food stamps and school lunches. Little fish like the National Aquarium. It's really all about the little fish.