Both immigration and Mexico itself were perceived as relatively small threats compared to more pressing concerns like cyberterrorism, Russia and China.
The measure, which would also stop federal officials from forcing some criminal veterans out of the country, failed to gain legislative traction last year.
The military services will start sending their backlogs of green-card holders to recruit training after a preliminary injunction issued in federal court.
A Mexican man living in the U.S. illegally must serve 20 months in prison for arranging immigrants to be smuggled by Fort Hood soldiers through a Texas border checkpoint.