Supreme Court Justice Samuel Alito compared asylum seekers who haven't made it across the border to a running back being tackled on the 1-yard line. | (Carlos Moreno/Sipa USA/Newscom) A 6–3 conservative majority of the Supreme Court ruled Thursday that the U.S. government can turn away asylum seekers who arrive at the border without processing their claims. The case, Mullin v. Al Otro Lado, was one of the closely watched immigration cases of the current Supreme Court term.