Much of the Reagan administration's credibility is riding on its advice that Americans can fly safely without the services of 12,000 air traffic controllers who were fired for taking part in an illegal nationwide strike.

"It's really not a 'Reagan problem' . . . but that's the way it'll be interpreted if two planes come together. If Reagan can live through this without a death, he's got it made," says John B. Galipault, director of the Aviation Safety Institute, a nonprofit, flight safety research group in Worthington, Ohio.

The administration also has laid its cards on the table regarding unions in the federal sector, whose leaders are watching the handling of the Professional Air Traffic Controllers Organization walkout with intense interest and more than a few misgivings.

For the moment, the Reagan team appears to be getting high marks from the public. It has presented itself as a tough, decisive management unwilling to accept violations of the law or what it considers outrageous demands from labor. A Newsweek poll shortly after the controllers walked out Aug. 3 showed that 57 percent of the American people support the administration's actions.

But with its insistence that all is well aloft, that the system is working fine with reduced manpower, the administration may have painted itself into a corner as tight as that now inhabited by the union.

Galipault's viewpoint may be open to some question -- much of his private funding is said to come from PATCO, a charge he denies.

Galipault says he is "arms' length from everybody," and he calls himself a Reagan supporter who believes the controllers "made a bad mistake" by striking. But he also says he is worried.

Since the strike began Aug. 3, Galipault's organization has received 175 "reports of incidents or hazardous conditions" involving flying aircraft. Thirty of those reports, including nine "near-misses," have been verified by his institute, Galipault says.

"We don't have any facts and neither does the Federal Aviation Administration. But the point is that when the FAA says there is nothing wrong going on in the system, that's like saying there never will be a Three Mile Island.

"You can have as many 'near misses' as you want, as long as two planes don't come together," he says. "If two of them come together, that's what you're going to hear about."

Meanwhile, Reagan's legal attacks on the controllers' union, particularly his push to strip PATCO of the right to represent its members, is seen by some union leaders as putting the future of federal sector unionism on the line.

Administrative law judge John Fenton has recommended, as requested in an administration petition, that the union's "exclusive recognition status" be revoked. If the three-member board of the Federal Labor Relations Authority goes along with Fenton, it would be the first time that a national public union has been decertified.

Nearly 1.7 million federal workers are represented by labor groups or associations. While public sector labor leaders aren't willing yet to say what effect the government's actions are having on their members, they agreed in interviews that two extremes are possible:

Unionized government employes could be cowed, and therefore more reluctant to challenge Reagan or any future president.

Or they could be galvanized, and thus become more militant in a way peculiar to people who believe they have been pushed too far.

"It could go either way, but I don't think anybody is going to be a total winner in this thing," says Gary Dinunno, spokesman for the American Federation of Government Employes, which represents 700,000 federal workers.

Uneasiness already has begun to set in, as exemplified by some federal employes' reaction to current contract talks on three fronts-- the Veterans Administration, the Social Security system, and the Air Force logistics command, Dinnuno says.

He believes the talks, affecting nearly 300,000 of the workers represented by AFGE, are going badly. "We're really running up against the wall with management in these negotiations," he says.

Other AFGE officials say their members are concerned that the administration is planning to do to them what, with much assistance provided by the controllers' illegal strike, it did to PATCO.

"Our members are very aware that we're standing in line right behind the controllers," one AFGE official says.

The first indication of federal union sentiment may come in the case of the postal workers, employes of an independent federal agency, the U.S. Postal Service.

Workers represented by the Postal Service's two largest unions, the American Postal Workers Union and the National Association of Letter Carriers, are voting on a new contract with the federal government. The balloting ends Aug. 24, and leaders of the two unions are anxiously awaiting the results, which they say could be influenced by the PATCO situation.

"We were confident that we would win the contract vote before the PATCO problem developed," says an NALC official who requested anonymity. "But it's impossible now to say exactly what will happen, what the effects of PATCO will be on our members and on the other federal workers."