No. Don't postpone. Walk-in to the district office where you interview was originally scheduled, ask to see a supervisor, explain your emergency and ask to be interviewed that same day.
Tell them you are flexible and willing to wait until called.
You'll get interviewed that same day. Just show that you are persistent and will not give up.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
It is unlikely that you will get a walk-in appointment, but you should go to your local USCIS office on the next day they are open. They will likely have information in the lobby for individuals whose interviews did not take place because the office was closed. Most likely, they will tell you that you will be getting a letter in the mail advising you of your re-scheduled interview date.