Local and national union leaders yesterday said they actively would suppor striking air controllers, because they fear President Reagan's strong stand against the illegal strike is an antiunion administration signal in support of big business.

But as national AFL-CIO President Lane Kirkland joined a Professional Air Traffic Controllers Organization picket line, steelworkers at a tavern in Baltimore, District firemen and Washington construction workers had mixed opinions about the strike, some supporting Reagan and some backing the union.

"I say fire them," said William F. Hyde, a 17-year veteran of the District fire department. "They're complaining about making $35,000 a year? I make $24,300. We're not allowed to strike, and neither are they. We don't like our pay situation any more than they do, but you don't see us out on strike."

"Yeah," added John Di Pietro, 40, who was sitting with Hyde at a table at Engine Co. No. 1, on M Street NW. "We're all sitting on a powder keg. The air controllers are not under any more pressure than the police or fire department. Let them run into burning buildings for a living and see how their nerves stand up."

But Michael Goode, a 23-year-old carpenter working at a construction site at 14th Street and Vermont Avenue NW, said he sided with the controllers. "To me, $30,000 or $40,000 a year is a small salary -- even though I only make $20,000 -- for the kind of pressures they have to deal with every day. A man's got to do what a man's got to do."

Most labor leaders agree with Goode. Yesterday, leaders at seven national and local unions -- including AFL-CIO, AFSCME, the American Federation of Government Employees, the United Food and Commercial Workers and the United Steelworkers -- said they strongly supported the PATCO workers' cause.

Other union officials said they have offered to staff PATCO strike headquarters and supply food and financial support to strikers and their families. Sympathy strikes also have been mentioned as a possiblility, although a spokesman for the AFL-CIO said a general strike of its 15 million members is unlikely.

A final decision on the possibility of a general strike will come out of the regularly scheduled executive council meeting fo the AFL-CIO in Chicago, where the air traffic strike is being discussed.

Several local unions yesterday sent members to Baltimore-Washington International Airport to join PATCO picket lines. Many unions have grounded their officials and asked their members not to fly out of airports that are being picketed.

Many union officials who will be attending a labor conference next week in Georgia have decided to drive rather than cross PATCO picket lines at airports.

"The events leading up to this confrontation and the repressive measures taken since, lead to the unmistakable conclusion that the Reagan administration is intent on breaking PATCO and all it stands for," said Kenneth Blaylock, AFGE president.

"If FAA were operating in the private sector they would have faced charges of failure to bargain in good faith from the National Labor Relations Board," Blaylock said. "Instead, they enjoy the full force of federal legal machinery and the judicial system in attempting to stifle the legitimate demands of PATCO and the workers it represents."

"We must ask who is the more blatant law-breaker," Blaylock said.

"I think [Reagan] forced the strike so he could show big business that he can and will beat up on union workers," said Thomas McNut, president of UFCW Local 400 in Baltimore.

"I get a strange feeling that our democracy is seriously being challenged when the administration says, 'Either you work or we'll destroy you economically,'" said David Wilson, director-elect of District 8 of the United Steelworkers said.

Though the air controllers, as federal employes, legally cannot strike, union officials said that these employes should be allowed to strike.

"Historically, when American have been confronted with laws that are unfair and unjust, they have ignored them," Thomas Bradley, president of the Maryland and District AFL-CIO, said. "That's how the labor movement began."

The labor movement that began with the heady defiance of laws called unjust lives today in such hometown taverns as the Jolly Post, a workingmen's bar with Budweiser curtains on the windows, hunkered in the gritty shadow of the Bethlehem steel plant in Sparrows Point.

The opinions about the air traffic controllers' strike there are as divided as they are vehement.

"I've always been a good union man, but [PATCO] is going too far," said Harry Hill, a 54-year-old maintenance supervisor at Bethlehem. "If you're a government employe, you signed an oath not to strike. Nobody twisted their arms."

Huey Walton, 50, a crane operator, disagreed. "If you pay union dues, what good is it if you can't strike? 'Round here, the union's all you got." CAPTION:

Picture, WILLIAM F. HYDE " . . . you don't see us out on strike."