For the second time in less that two weeks, a federal union has raised the specter of using an illegal strike to win its demands from the government.

The latest threat comes from the nearly 15,000-member Professional Air Traffic Controllers Organization, a tightly knit group regarded by many labor observers as the most militant of federal unions. It would be PATCO's first nationwide walkout, although the union has made use of regional and national sickout and slowdowns.

The first challenge came from the Postal Service's two largest unions, the American Postal Workers Union and the National Association of Letter Carriers, collectively representing about 500,000 members. Those groups signed a tentative agreement with the government July 21, after making a series of highly qualified, last-minute strike threats.

PATCO's threats have been neither qualified nor last minute. The union published a strike manual more than a year ago, on April 15, 1980, and it came within 5 percent-age points of voting to walk off the job June 22. The union's leaders got a 75 percent strike authorization vote when 80 percent was needed. They also got a tentative agreement scant hours before a strike deadline.

That agreement was rejected last week by a 95.3 percent vote of the PATCO membership, which has led to the current crisis.

The postal workers could have slowed the mails and might have put some marginally profitable mail-order houses out of business. But airline industry officials say, and federal officials such as Transportation Secretary Drew Lewis agree, that a strike by the controllers could severely curtail domestic commercial air traffic and do billons of dollars of damage to the national economy.

That is why Lewis and other government officials have been adamant in their opposition to what Lewis has called the controllers' "outrageous" economic demands and their "unreasonable and irresponsible" use of the strike threat.

But controllers interviewed yesterday and last week say that if the government hasn't met their demands, they are determined to be on strike this morning, in defiance of the president of the United States, the attorney general, more than half of the Senate and many members of the House of Representatives.

Some of them, perhaps their leaders, may be put in jail. Individual PATCO members who walk off their jobs in defiance of federal law could also be imprisoned for a year and be fined $1,000. They could lose their jobs, which pay up to $49,229 annually, depending on experience and position. They could lose any future chance of federal employment.

And their 13-year-old union, the largest subsidiary, of the National Marine Engineers' Beneficial Association, could be broken, with a lasting effect on the already troubled future of collective bargaining in the federal government.

Many members of the union think those risks are worth taking. Among them is Michael Fermon, PATCO eastern regional vice president.He is 35 years old and has 11 years' experience as a controller, most of it at Boston's Logan International Airport, one of the nation's busiest.

When he took leave from active duty two months ago to assume his current position, Fermon was a GS14, the highest controller rank, earning "in the forties," he said.

"Maybe we are crazy," Fermon said. "But I'd like to turn that question around. Why would a group of people, with all of the threats and rhetoric being made against them, with everybody in government saying what they're going to do to them, go out and break the law? If we do that, don't you think it means we have serious problems in our occupation? You think we just decided, all of a sudden, to take a chance and just throw everything away?"

Fermon says the controllers' militant stance is a result of frustration: "They are so angry, so frustrated, so fed up that the government is going to have to come a very long way to get this thing solved."

The frustration, Fermon said yesterday, comes from not being able to work the years required to become elibible for full retirement benefits. "Burnout" -- a stress-induced condition manifested by disabling physical and/or mental problems -- causes many controllers to leave their jobs years before full retirement eligibility, the controllers say.

The controllers also complain that they receive too few sick days. They get 13, the same as all other federal workers. Other federal workers, however, can take medication to relieve the symptoms of their ailment -- a head cold, for example -- go to work and save their sick days for a more serious ailment. But Fermon says, in a statement verfied by the Federal Aviation Administration, "We are not allowed to work at our jobs if we take any kind of medication. That usually means using a sick day that another federal worker can save."

As a result, PATCO is seeking 26 sick days annually. The union also is asking for a shorter workweek, which it claims will enable its members to better cope with stress and increase their longevity on the job.

"We've been asking for these things for 13 years. It's nothing new," Fermon said. "But all we got in 13 years was lip service. Well, lip service is no longer acceptable."

Nor, says the government, are PATCO's demands. Lewis says PATCO's proposals would cost at least $681 million annually, unacceptable to a government only willing to offer $40 million. Lewis has called the demands "outrageous . . . an affront to the American public."

But, according to David A. Trick, PATCO director of operations, it all comes down to this: "If we're right, we'll win. If we're wrong, we'll lose."