Craig Martin, a computer programmer trying to return to Denver, is sitting at National Airport's North Terminal just outside the People Express gate. He is guarding 12 boxes he would like to check. People Express won't take them off his hands because it is more than an hour before his flight and baggage-handling personnel are scarce.

"United would let me check them, and I could go sightseeing," Martin says. His company booked him on People Express because the price was only $89, or $178 for a round trip. The usual round-trip fare on United Airlines is $245. "I doubt the company will fly People Express again. Our company president was along on this trip, and he didn't like it any better than I did," says Martin.

People Expresss just lost two business travelers, the type it must attract and keep if it wants to serve big-league markets and enjoy financial stability. Baggage check-in and predictable schedules are in short supply at People Express, which trailed only World Airways and Pan American World Airways in complaints per 100,000 passengers filed last year with the Transportation Department.

Donald C. Burr, People Express' founder, chairman and only significant decision-maker, has now admitted in public what analysts and others in the airline industry have been saying for months: The airline is in trouble. The generally accepted explanation is that People Express tried to expand too rapidly without building the necessary management.

In a statement released last Monday, Burr said that People Express "is currently exploring a variety of different possible courses of action including steps to further increase its revenue, a plan to produce significant cost savings and sale of specific assets. In addition, in light of the continuing consolidation in the airline industry, the company . . . also is exploring the possible sale of parts or under certain circumstances even all of the company."

The word is that People Express is in a severe cash bind. It had a $58 million loss in 1985 and an $18.8 million loss in the first three months of this year. Some estimates put People Express' balance as low as $60 million -- just $10 million more than Frank Lorenzo had in 1983 when he took Continental Airlines into bankruptcy.

Burr and other People Express officers did not return phone calls. However, Burr said in a recent interview in Travel Weekly, "We have about $100 million in cash." He said that investors "are unhappy with me right now, and for good reason, because we haven't made enough money. And I am the head singer in that chorus. So we need to make some money and we need to add to our cash levels. Nothing is new about that."

Soon after that interview came a new low-fare campaign and the announcement that at least part of People Express was for sale.

This is the airline that revolutionized the industry with a low-fare, no-frills philosophy. People Express started in April 1981 with three airplanes and 250 employes. It now has 79 planes and 3,500 employes and a route network that extends from Los Angeles to London, with all flights meeting at its base in Newark.

People Express' nonunion employes are paid less than many of their counterparts at other airlines and are expected to do more than one job. Flight attendants sell tickets and load baggage, for example. All employes are called "managers" and are required to own at least 100 shares of stock in the company.

Executives, including Burr, do not have secretaries and, like other managers, are expected to help out on the line. It is either very democratic or "loony-type cultism," in the words of a senior executive at another airline.

The formula worked while People Express was small, but its early success drew the map for established carriers with mature management structures. It didn't take the Uniteds and Americans long to drive down their own labor costs and selectively match People Express' low fares while providing more amenities and avoiding the old Newark terminal through which People Express funnels almost all its passengers.

John V. Pincavage, analyst for PaineWebber, said, "I don't think they're in any real immediate danger of going under, but the announcement they put out is going to make the hole deeper to crawl out of, because people book away and competitors are not going to give them an inch. The other guys in the industry are like vultures sitting on a fence post; this guy needs a drink of water" and they aren't going to give it to him.

David Sylvester, an airline analyst with Montgomery Securites in San Francisco, recommended in November that investors sell their People Express holdings, shortly after Burr won a takeover battle with Lorenzo and acquired Denver's failing Frontier Airlines. Sylvester said then that "the Frontier acquisition increases the risk" for People Express but would do little to enhance People Express' short-term future.

Last week Sylvester said he thinks Burr's announcement is "the end of People Express as we know it. One of several things can happen: The whole company can be purchased by another airline and you would see a radical change in the way the company does business; you could see a sale of part of People Express, the Frontier part or the 747 part the airline's small fleet of Boeing 747s and its trans-Atlantic routes , or you could see new management."

Frontier, an old-line unionized airline that was in desperate financial trouble when People Express acquired it, has not taken well to People Express' different approach, and it continues to lose money. Pincavage and other analysts suggested that the first thing Burr might want to do to raise cash would be to sell Frontier's 24 gates at Stapleton International Airport in Denver and maybe Frontier's maintenance facility for Boeing 737s. The rest of Frontier is regarded as valueless.

United and Continental compete fiercely in Denver, and both were reported to be negotiating with Burr for some of those gates, but none of the principals would comment.

If the future for People Express is bleak, it has earned a major role in the history of the airline industry, deregulated by Congress in 1978 and thus stripped of its protection from innovators.

"You would have to look upon People Express as a pace-setter," said George James, of Airline Economics Inc. With its low fares, People Express "definitely tapped new markets, latent markets -- people who because of income levels might not otherwise have traveled," James said. People Express fares were actually lower between some cities than those of Greyhound and Trailways, and customers lined up to buy tickets.

Despite the attractive prices, however, passengers discovered that the People Express hassle level was high. The airline is notorious for overbooking and for flight delays at Newark. It is sometimes difficult to reach the company by telephone. At first, Burr alienated travel agents -- who write about 80 percent of tickets sold -- by not paying commissions. Even today, People Express tickets cannot be written on many of the computer reservation systems that most travel agents use, thus reducing People Express' accessibility.

With other carriers selectively emulating People Express' fares, People Express was forced to return the compliment by seeking more business travelers. It has started a frequent flyer bonus program and is beginning to sell more than one class of service and to make checked baggage a bit more welcome.

Burr told wire service reporters last week the new low-fare campaign brought back passengers, and Joe Mysliwiec, one of People Express' two managers permanently stationed at National Airport, said that has been his experience.

He answered questions between battles with a broken-down reservations computer and an irate customer. "I have confidence in our company, it's going to go up," he said. "If I didn't think so, I'd be looking for another job."