It might have been worse - much worse - than the usual traveler's nightmare.

The 5 p.m. Eastern Airlines shuttle from New York to Washington had been sitting on the La-Guardia runway for more than an hour Tuesday evening. One passenger counted 38 planes waiting in front of it for take-off. The cabin temperature was rising. The passengers were sweating and grumbling.

In Washington, at the same moment, a 27-year-old man was waiting in the Howard University Hospital for a small piece of cargo being carried on that flight - the key to his survival.

Strapped into one of the front seats was a little machine, and inside it were two kidneys that had been removed tha night before from a young man who had died at St. Luke's Hospital in Manhattan.

After tests had determined Tuesday afternoon that one of the kidneys might be suitable to be transplanted into the patient, St. Luke's technician Michel Jean-Jacques had placed them in a preservation machine to take to Washington.

Rush hour traffic kept him from reaching La-Guardia until after the 4 o'clock shuttle had left. At 4:20 he carried the 50-pound machine on board the next flight. At 6 p.m. the plane was still sitting on the runway.

"It was a scary situation," the Haitian-born Jean-Jacques said, "Knowing I was carrying an organ to save somebody's life. The risk was great. I was losing my power on the machine. The life of the battery is not more than five or six hours, and it was very hot, you know. Because of the heat the battery had to work much harder."

Finally Jean Jacques informed the pilot, C. G. Russ, of the situation. After a brief further delay, the plane was allowed to taxi past the other planes waiting in line and take off. At Washington it was cleared for a landing almost immediately, despite the horrible weather conditions.

Dr. Clive Calendar at Howard had scheduled the operation for Tuesday night, and as he waited he grew increasingly apprehensive. The longer a kidney has to survive on a machine, the greater the chances of possible complications.

"We anticipated that there would be problems," Calendar said - problems that might have prevented the transplant and condemned the patient to months of more waiting for another kidney, while he was kept alive with a kidney dialysis machine. The man's kidneys were removed six weeks ago.

"Fortunately," Calendar said, "we were pleasantly surprised."

The patient entered the operating room at 7 a.m. yesterday morning and emerged 6 1/2 hours later, according to Calendar, with his one new kidney functioning well.

Jean-Jacques, meanwhile, had flown back to New York with the second organ, which, he said, is still in good shape. Today, it is hoped, it will help save the life of another man - who is flying to New York from Italy.