The policy was due to expire on 21 December, but has won a temporary reprieve from the Supreme Court.
On Monday Chief Justice John Roberts temporarily blocked its termination pending a ruling on an emergency appeal from some Republican-led states who have asked for the policy to remain in place.
The court"s intervention, however, has meant little on the streets of El Paso, where shelters and humanitarian services have already been overburdened and weary migrants left sleeping rough in bitterly cold nights.
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