In Bloomington, Ill., machine shop Mechanical Devices can't find the workers it needs to handle a sharp jump in business. Job fairs run by airline Emirates attract fewer applicants in the U.S. than in other countries. Truck-stop operator Pilot Flying J says job postings don't elicit many more applicants than they did when the unemployment rate was below 5%.

With a 9.5% jobless rate and some 15 million Americans looking for work, many employers are inundated with applicants. But a surprising number say they are getting an underwhelming...