The situation could be particularly complicated for asylum-seekers from countries like Venezuela, which doesn’t have diplomatic ties with the U.S.

Venezuelan Josnexcy Martinez, who is staying at a shelter in a Texas border city, said she's afraid of getting swept up in a raid targeting migrants even though she entered the country legally.

According to NBC News, Senior U.S. District Judge John C. Coughenour heard 25 minutes of arguments and then issued an order from the bench blocking the policy from taking effect for 14 days.