Whether posing for photos at the Lincoln Memorial or strolling the grounds of Mount Vernon, the jet-lagged group that joined the tourist throngs in yesterday's mid-afternoon mugginess looked like any other visitors from Japan.

So why were so many people in the Washington area tour industry holding their breath?

Because these particular visitors hold the power to drop tens if not hundreds of millions of dollars on the Washington area. These were very senior people from Japanese airlines, tourism promotion offices, hotels and travel agencies -- the highest-powered such group to visit the area in years. They were here to inspect the local sights and sounds and decide if their fellow citizens would enjoy them.

The area tourist industry spared no expense or pain to try to make them decide "yes."

At Dulles International Airport Sunday, airports director Jim Wilding boarded their jetliner and zipped them through customs. At the Ritz-Carlton on Massachusetts Avenue NW they found Americana gifts (pewter cups, among others) in their rooms. And, in deference to Japanese superstitions, no one was put on the fourth floor (the Japanese words for "four" and "death" sound the same).

"We all are holding our hands up and want to be noticed by these people," said Richard J. Valerio, president of American Sightseeing International, a tour company association and host of the 30-member group at a breakfast yesterday. "The Japanese are critical to the future success of any of the hotels in this area," said Vivian Deuschl of the Ritz-Carlton.

About 150,000 Japanese visited the Washington area in 1989. They come from one of the world's richest countries and carry one of the world's most powerful currencies. Their numbers are rising. So, too, are foreign visitors to the United States in general. Last year, their spending reached a staggering $44.5 billion ($9 billion of it from Japanese), outstripping for the first time in recent years Americans' spending abroad.

Some analysts lament that shift as a sign of American decline. U.S. products are no longer competitive in world markets, they say, so all the country can do is rent time on its beaches and monuments. But many others see it as an economic growth engine as good as any other.

Tourism brings in foreign exchange, lowering the balance-of-payments deficit. It pumps up many facets of a local economy -- more hotel stays, taxi rides, banking services, restaurant meals, construction, phone calls, shopping and theater tickets.

Some economists see it as an export, in the sense the United States is selling a product -- leisure -- to foreigners. It has reached the point, said Rockwell Schnabel, head of the U.S. Travel and Tourism Administration, that "tourism is the number-one export of the United States." As a category, it is bigger than commercial aircraft, bigger than computers, bigger than farm goods.

Schnabel's agency promotes tourism here as a means of offsetting the overall U.S. trade deficit. It has an ally in the Japanese government, which is doing exactly the opposite: It is encouraging its people to travel abroad as a means of whittling down that country's huge surpluses. Last year, Japanese tourism here knocked about $6 billion off the U.S. deficit.

A "Ten Million Project," established by Japanese bureaucrats to get that many Japanese citizens to travel overseas each year, will be more than met in 1990, forecasts show. About 3.4 million (including heavy representation from Japan's honeymoon couples) are expected to visit the United States this year.

Like many Japanese industries, this one can be insular. Although this is changing, Japanese still often travel on Japanese airlines, stay in Japanese-owned hotels and tour with Japanese tour companies. U.S.-owned companies sometimes complain that they can only nibble around the edges of this business.

Why do they come? Many Japanese have a mystical image of the United States, drawn from television, books and the U.S. military occupation of the 1940s. To them, America is a land of great vistas, dazzling entertainment and small-town virtue. One traveler in fact, once told Commerce Department interviewers that he wanted to go to the United States "to meet a Mr. Jones or a Mr. Smith."

Those who visit Washington come for much the same things that attract Americans -- the White House (which they see on TV news at home almost as often as Americans do), the Capitol, the grave of President Kennedy, the Smithsonian museums. Talk of Washington as the "murder capital" hasn't done much damage -- New York and Los Angeles are rated in Japan as the real places to watch out for.

Isao Matsuhashi, president of the Japan Travel Bureau, said yesterday as he climbed the steps of the Lincoln Memorial that to him Washington is "the core of the United States, the feeling, the genuine American spirit. I can feel it."

The area tourism industry is promoting that role but also trying to persuade Japan that there is much more here than that -- shopping and nightlife, for instance. Today, the group will be feted at the Ritz-Carlton in Pentagon City, site of a lavish shopping mall, then move to Old Town Alexandria. Then on to Baltimore for a tour of the Inner Harbor.

From Baltimore, they will head to Florida and Georgia, where they will be hosted by people just as anxious for their business.

Whatever impression it has made, Washington can probably count on Japanese business rising. All Nippon Airways is about to go from six flights a week into Dulles to seven. And Japan Air Lines will soon inaugurate nonstop service. With new seats available, the airlines will find a way to fill them.