SAVANNAH, Ga. — A few years back, the heavy-equipment manufacturer JCB held a job fair in the glass foyer of its sprawling headquarters near here, but when a throng of prospective employees learned the next step would be drug testing, an alarming thing happened: About half of them left.

That story still circulates within the business community of this historic port city. But the problem has gotten worse.

All over the country, employers say they see a disturbing downside of tighter labor markets as they try to rebuild from the worst recession since the Depression: They are struggling to find workers who can pass a pre-employment drug test.

That hurdle partly stems from the growing ubiquity of drug testing, at corporations with big human resources departments, in industries like trucking where testing is mandated by federal law for safety reasons, and increasingly at smaller companies.