Final answer:
President Reagan's decision to fire more than 10,000 striking air traffic controllers had a significant impact by effectively destroying the Professional Air Traffic Controllers Organization and ushering in a new era where labor unions' influence was significantly reduced.
Step-by-step explanation:
The impact of Reagan's firing of the air traffic controllers was significant in setting a new tone for labor relations in the United States. After the air traffic controllers who were part of the Professional Air Traffic Controllers Organization (PATCO) went on strike for better working conditions and pay, President Reagan chose to fire over 10,000 of these federal workers. This decision not only ended the strike but also effectively destroyed PATCO. It marked a pivotal shift in labor relations where employers followed Reagan's lead, replacing striking workers, thereby leading to a deterioration of labor unions. These actions contributed to the leveling off of real wages for the average American family during the 1980s and represented a new era where labor unions had diminished influence.