The U.S. government's surprise offer, then abrupt reversal, of an opportunity for thousands of skilled foreign workers to obtain permanent residency in the U.S. highlights the problems of the overtaxed immigration system and the frenzy that results from a rare chance to apply for a green card.

The scramble has put tens of thousands of workers and their families in limbo after many of them and their employers spent thousands of dollars in hopes of securing permanent residency. It may result in a class-action lawsuit against...