LOVELAND, Colo.—Jerry Stooksbury, the president of Avionics Specialists LLC, needed to produce an airplane instrument panel last fall, but had only two employees able to complete the task quickly.

One was out sick. The other was in high school.

He called the high-schooler, 17-year-old Thayer McCollum.

Thayer, who starts his days drinking chocolate milk and blasting indie rock, works part time operating mechanical-drawing software for aircraft parts. He came in to do the project and still had time for homework.

After the longest stretch of continuous job creation on record—more than seven years—the U.S. faces its most severe worker shortage in the past two decades. Employers, from General Electric Co. and Michelin North America Inc. to a Wisconsin nursing home and an Ohio turbine-parts manufacturer, are expanding their hunt to the labor market’s youngest echelon.