On veteran astronaut John Young's desk sits a model of the space shuttle, which Young is to pilot on its first flight away from Earth. Like the model, the real shuttle doesn't move, and Young squirms with impatience.

"I figure by the time we get to fly I'll be 130 percent trained for the mission," Young said in a recent interview at the astronaut office at the Johnson Space Center. "We looked at the schedule on the first of April and 85 percent of our training squares were already filled. I've never been that trained before.I mean, all the missions I've been on before this we launched before we finished training."

Not this time, Shuttle managers at the Space Center now believe the first flight will come no sooner than March 1981, which puts it two years behind schedule. There's even a chance it won't go until June 1981.

"You don't get any kudos in this business for on-time failures," center director Christopher Columbus Kraft Jr. said in an interview. "If something else develops which changes our confidence in the vehicle then we're just going to have to delay it again and take the criticism, because we're not going to launch an unsafe vehicle."

The first shuttle flight has already been postponed six times, doing serious harm to the space agency's credibility. There's a growing concern in the White House and Congress that fresh delays putting the first flight deeper in 1981 could do permanent damage to the shuttle program.

"We running out of patience on the space shuttle," a White House source confides. "There's a feeling here that we con't tolerate any more delays in the shuttle program."

One reason is that delays cost money. Take the silica tiles being placed, one by one, on the shuttle's airframe to protect it from the blistering heat of re-entry into Earth's atmosphere. The space agency wanted most of the 30,922 tiles placed on the shuttle when it was shipped from Palmdale Calif., to Cape Canaveral, Fla., in March 1979. The shuttle left Palmdale with no more than 10 percent of its tiles in place, some of which fell off on the trip to the Cape.

Shuttle managers quickly assembled a force of 1,200 people to install the tiles. Working two shifts of 10 hours six days a week at the Cape, they are still 5,000 tiles short of completing the job. The delay is costing the space agency $1.3 million a week.

Shuttle accountants now estimate that by the time the first one flies, they will have spent $264 million on the solid rocket engines, $381 million on the tiles, $442 million on the external fuel tank and $1.5 billion on developing the main liquid rocket engine.That adds up to an overrun of almost $1.6 billion.

There's a more urgent reason behind White House and Congressional concern. The space shuttle is the first civilian spacecraft that will put into orbit the Pentagon's surveillance satellites, at least two of which are scheduled for flight in April and May 1983. If the first shuttle test flight slips later than March 1981, the surveillance satellites won't get into orbit on time.

The surveillance satellites due to fly in 1983 are the biggest and most sophisticated ever built. As large as 25 tons apiece, they were designed by the Pentagon for the shuttle. They are too big to be carried into orbit by any other rocket, not even the Titan 3-D used by the Pentagon as its workhorse engine to lift heavy payloads into space.

"If these satellites can't fly on the shuttle in 1983, they will have to be downgraded to fit on the Titan," said Sen. Harrison H. Schmitt (R-N.M.), the former astronaut who is the ranking Republican on the Senate subcommittee on science, technology and space. "That would be hard to take, in light of today's conditions, which make surveillance satellites all that more important."

When the shuttle began in 1971, two technological challenges stood out that engineers thought could delay the program.

One was the reinforced carbon material for the nose cap and leading edges of the wings, which had to take 2,800-degree temperatures on re-entry. The other was the in-flight computer, four of which would be built into the shuttle to "talk" to one another 440 times a second to make sure that none of the other computers was forgetting anything or making any errors in space.

"Neither one of those things has given us any trouble," Orbiter program manager Aaron Cohen said in an interview. "They've turned out to be beautiful."

Not so beautiful have been two other technological challenges, the main rocket engine that burns liquid hydrogen at 3,000 degrees and the silica tiles that cover the airframe to protect it from re-entry temperatures of 2,400 degrees.

Consider the shuttle's three hydrogen engines, each 10 times as powerful as the largest jet engine. The pumps moving fuel into the engine chamber spin at twice the speed of any pump built before. Fuel burns in the chamber 1,000 degrees hotter than any engine before it.

"These engines are also the first liquid rocket engines designed for re-use," shuttle program manager Robert Thompson said in an interview. "We had to expect that, in heating it and stressing it with repeated use, we were going to run into problems."

Thompson said the "problems" have cost the agency an extra year of test time. Engines have caught fire and even blown up during tests. No fewer than six of the last 12 tests of the three engines firing together had to be stopped because of engine overheating. By the expected end of engine testing late this summer, it will have cost $1 billion more than the $500 million the agency thought.

More worrisome are the tiles to protect the aluminum airframe from aerodynamic and re-entry heating. At times the shuttle will fly 26 times faster than sound; a new way had to be developed to handle the heats generated by those speeds.

"We had to come up with something as light as balsa wood that could take temperatures of 2,400 degrees," manager Cohen said."It also had to be reusable; we couldn't afford to throw it away each time the shuttle came back from space."

The result was the silica tiles, whose development, production and installation has been a technological nightmare. To begin with, not two tiles are the same. They're all custom built to fit a specific part of the shuttle's fuselage. Furthermore, installation is painstaking -- 25 hours to fasten a single tile.

"We discovered after a lot of the tiles were on that half of them had lost their strength in the process of being bonded to the shuttle," Cohen said. "We had to pull those tiles off and paint a liquid glass on the back of the tiles to get their strength back."

The 1,200 tile workers at the Cape are now putting on 750 a week, but are taking them off at a rate of almost 100 a week. About 5,000 cavities on the shuttle frame remain to be filled, a job Cohen hopes will be finished by the end of August.

In fairness to the space agency, the delays caused by engine and tile troubles are not all its fault. Testing engines was held up one year because Pratt & Whitney sued the agency when it lost the engine contract to Rocketdyne. Tile tests were also delayed a year because of money shortages.

"We tried back in 1978 to cut back on the way we spent our money," center director Kraft said. "The result was we delayed building the tiles, and that naturally delayed our test process which naturally delayed us from getting at the answers we now have."

Despite all its delays, the shuttle is on its way to becoming an economic success. Space in the 60-foot-long cargo bay is sold out for all but three of the first 40 operational flights. By the end of next month, there may not be any room lest at all for people who want their satellites shuttled into space.

"We're looking at a manifest right now that says we may be booked solid right out to late 1986, which is 68 operational flights," payload manager Robert Everline said. "That's fooled everybody."