Humane societies around the country tried to send in their own people to save the pets (photo below).
The official rule during Week 2 was, "Ignore all animals and go for the holdouts/survivors" (and corpses).  I have seen many photos of dogs on the porch, dogs on the roof, watching the rescuers go by. 

I grieve to see broken bonds and betrayal, whether of one mammal to another, or of a government to its people.  
(above)  A dog hides under the bench of a military truck on 9 September, after the evacuees have filed off.  Presumably it saw a crowd and followed the legs. 

(left) This dog has never seen Jane Garrison before, and it has zero language skills with which to express its understanding of the situation.  Then again.....   The Human Society of the United States had volunteers in New Orleans on Friday, 9 September, Day 12. 

Highly-trained corpse-and-survivor-spotting dogs had to be decontaminated after searching.  Here, "Georgia Search and Rescue Central K-9" is working Violet, Louisiana on 9 September.  (center)  Debbie Goebels and Ryca..  (right) Paula Chambers and Madison.  Four rescue dogs have died from the toxic floodwaters as of 11 September.  First Deputy Mayor of Baltimore, Michael Enright,  leading a contingent of 150 first-responders, has decided no to use his inflatable Zodiac boats for fear the floating petrochemicals will destroy the rubber. 

If you think that, sitting on the couch, you can train a dog to stop dead in its tracks on command, go to the door, sniff a new arrival,  and come to your side if asked, then you can play the rescue game.  But it cuts both ways.  Whenever the dog comes to your side, you must respond.  If you are working an earthquake site and the dog comes back to your side, you must follow  it to the cadaver.  If you tell your companion you are not interested (actions speak louder than words), you are not going to get a follow-up e-mail.