Revving up America's space shuttle program to full speed may not be easy, given the Reagan administration's budget-cutting mood. National Aeronautics and Space Administration (NASA) information chief William J. O'Donnell blames ''severe financial constraints'' for the engine problems which have set back shuttle launch schedules this year. ''We simply haven't had the funds to do the tremendous amount of testing that we used to do on new developments,'' he insists.
One possible result, Mr. O'Donnell adds, is that the shuttle could lose more customers to the European Space Agency's competing unmanned Ariane rocket which, he says, ''has already taken some customers from us.''
But despite a 10-week delay due to engine leaks and cargo bay contamination, NASA's second reusable shuttle orbiter, Challenger, has been cleared for its maiden flight April 4. If this sixth Space Transportation System mission (STS-6 ) is completed without any further ''glitches,'' NASA expects to be back on schedule for launching STS-7 in mid-June, STS-8 in early August, and the European-built Spacelab payload on STS-9 in late September or early October.
''If we are back on schedule with STS-9,'' says NASA's shuttle-program head, Lt. Gen. James A. Abrahamson, ''then we will have demonstrated a major recovery by taking on a difficult problem and solving it.'' The problem has been complicated, he explained recently, by ''reduced funding levels.''
NASA officials point out that after the agency pared its programs to what it considered absolute minimums, the administration still trimmed NASA's 1984 budget request by $615 million, to $7.1 billion. This 4 percent increase over 1983 spending, NASA officials say, doesn't even keep up with inflation.
Bruce Abell, spokesman for the White House Office of Science and Technology, says that the administration position is that support for any NASA budget increases must wait ''until we see good, solid proposals which would justify more spending.''
But space-flight experts contend that the shuttle program already has proved its military and commercial worth enough to justify increased funding.
Congressional Research Service aerospace specialist Marcia Smith says that NASA has suffered from years of underfunding. While she expects Congress to continue pushing for larger NASA budgets than the Reagan administration wants, she warns that a sudden infusion of funds will not produce instant results. ''You can't just throw money at NASA now when the problem has been lack of money for the past 10 years,'' she says.
Ms. Smith says that STS-6 has experienced delays not because of NASA failures , but simply because Challenger is ''a new bird which has never been flown before,'' and carries new higher-thrust engines.
Jerome Pearson, an aerospace engineer at the Air Force Flight Dynamics Laboratory at Wright-Patterson Air Force Base, also blames shuttle problems on tight budgets. Noting that ''the NASA budget peaked in 1966 and has been going downhill since then,'' he says despite funding problems, ''I think the shuttle program will turn out to be profitable and enormously successful.''
After his early concern that Challenger's engine problems ''might require complete redesign,'' Mr. Pearson says his only remaining concern is that, due to budget cuts, ''we're not aggressively developing the shuttle's tremendous capabilities.'' He criticizes the Reagan administration's decision to cut back on the number of shuttle flights, its cancellation of plans for a fifth shuttle vehicle, and its lack of support for building a permanent space station to match the one he expects the Soviets will orbit in the near future.
Cutting back the shuttle program, says Pearson, is a shortsighted approach which ''is sending signals to potential customers that they can't depend on our space shuttle program.'' America's shuttle has many advantages, he points out. But if tight budgets continue to rein in NASA's best efforts while the Soviets, French, and Japanese actively upgrade their own space delivery systems, ''our advantages may begin to disappear,'' he adds.
The shuttle's problems to date ''represent normal and should-have-been-expected occurrences that go with any kind of experimental vehicle,'' says Willis Hawkins, a senior adviser for the Lockheed Corporation, one of many contractors on the shuttle project. Mr. Hawkins, who has worked closely with US space, aircraft, and missile programs, adds that ''nothing that has happened in the shuttle development process should deter us from pursuing this program.''
He describes the shuttle as ''the most straightforward approach to putting things into space economically.'' But development problems have cropped up, he says, because NASA is a government agency operating on an annual budget. Instead of funding a long-range development program as a commercial organization would, ''NASA has to fight for its money year by year'' he says. Along with having its own budget cut, Hawkins adds, ''the shuttle also suffers when budget cuts in other areas cut back on the number of customers buying payload space on the shuttle.''
He says shuttle funding should be increased to make design changes that would incorporate the latest technology. ''NASA and a lot of us outside NASA would like to make systems changes which would improve the shuttle's operational reliability,'' he says. ''But this is a very expensive proposition, and NASA is making some hard decisions now on which systems they can afford to change to make the bird more operationally suitable.''
Hawkins says that years of tight budgets have left NASA with a shortage of spare parts. ''The result,'' he explains, ''will probably be some further delays depending on the life of the experimental parts NASA is forced to use.''