Union officials, keeping a close watch on the air controllers' strike, are showing a growing concern over the possible effects of President Reagan's hard-line labor policies.
Members of the AFL-CIO executive council and presidents of unions meeting in Chicago Aug. 6 affirmed their support for the Professional Air Traffic Controllers Organization (Patco) in its showdown with the federal government, but many of them talked frankly of the implications for the US organized labor movement.
Union leaders see these problems ahead:
* Public employee unions are afraid precedents will be set for city and county governments when employees strike.
* Unions in the private sector, particularly those looking ahead to contract bargaining in 1982, fear that private employers -- already turning more conservative in their approach to unions -- might now be encouraged to reflect the Reagan position and negotiate more stubbornly.
* AFL-CIO unions with important legislation awaiting action on Capitol Hill after the midsummer recess see new problems ahead as many senators and House members react against Patco's defiance of the government.
Lane Kirkland, the AFL-CIO's president, denounced the Reagan administration stance as "strike breaking" and "union busting." But the federation's executive council limited its support of the walkout to a resolution of support and an hour's picketing at Chicago's O'Hare airport.
Individually, the members of the council and union presidents were unanimously angry at Mr. Reagan's tactics but reluctant to back the Patco walkout -- illegal under federal law. Many apparently felt that the controllers , no matter how valid their dissatisfaction with the bargaining, had brought on potentially serious problems for all labor by striking without first seeking a compromise settlement with the government.