What does Reagan’s treatment of the striking air-traffic controllers reveal about the United States government’s attitude toward organized labor?
I really don't think one can claim that this 1981 action by President Ronald Reagan, in which he had the striking controllers fired for going on strike in the purported interest of public safety and had new ones hired to staff the air traffic control system (I remember it because I was a student at the time myself), is indicative of "the United States government’s attitude toward organized labor" as you stated in your question since Reagan's administration, though politically conservative and thus generally less inclined to support workers vis à vis management, was only one of many in U.S. history, and indeed subsequent presidents such as Bill Clinton and Barack Obama have had notably much more favorable dispositions toward organized labor.
And of course "the United States government" encompasses a lot more than just the Executive Branch and its head, namely the President, and indeed Congress has passed a large amount of labor-friendly legislation through the years (and mostly upheld by the federal court system including the Supreme Court) a lot of which was rooted in the concept that workers have the right to organize and strike for better working conditions. And the U.S. federal government has many agencies (e.g. OSHA, the Occupational Health and Safety Administration) directly instituted or charged with the oversight of labor issues through these laws passed by Congress that clearly are actively supportive of the goals of organized labor and workers' rights.