Complete court ruling: "These competing public interests do not justify a stay."

Finally, in evaluating the need for a stay, we must
consider the public interest generally.
Aspects of the public interest favor both sides, as
evidenced by the massive attention this case has garnered at
even the most preliminary stages. On the one hand, the
public has a powerful interest in national security and in the
ability of an elected president to enact policies. And on the
other, the public also has an interest in free flow of travel, in
avoiding separation of families, and in freedom from
discrimination. We need not characterize the public interest
more definitely than this; when considered alongside the
hardships discussed above, these competing public interests
do not justify a stay.

Conclusion
For the foregoing reasons, the emergency motion for a
stay pending appeal is DENIED.

http://cdn.ca9.uscourts.gov/datastore/opinions/2017/02/09/17-35105.pdf