If you have no problem with your tax dollars going to aid them then you'd have no problem donating to them of your own free will. Not to mention that he's absolutely right that they should have insurance to cover them.
My heart goes out to the victims too, most especially those I know personally. We immediately give a little extra to private relief agencies who move in immediately to help those who have suffered property damage, injuries, or loss of loved ones. Our Mennonite friends who go to all disaster areas at their own expense and to help in any way they can are already there.
Once you take emotion out of it, however, and replace that with solid common siense, certain principles must apply for a free people:
The house that burned down in your town last night was just as devastating to the occupants as those caught in the tornados. Why is one more worthy of government rescue than the other?
If you choose to live in a place in which earthquake, hurricanes, large hail, heavy snows, tornados, land/mud slide, avalanche, devastating floods, etc. are essentially non existant--Albuquerque or Phoenix for instance--why should you be liable for risk chosen by people who do live in areas where such risk does exist?
My house is insured against fire, wind, hail and other natural or possible perils. Because we now are in an area essentially immune to flood damage and a damaging earthquake is highly unlikely in our lifetime, we do not have flood insurance or earthquake insurance. When we have lived in areas where flooding was a possibility we did have flood insurance, and if we moved into an earthquake prone area, we would expect to acquire earthquake insurance. It is what responsible people do. My loss should not be your responsibility to take care of.
Homeowners and business owners should be responsible to insure their property or take their chances. If they don't have insurance and sustain severe loss, they will be out the money or they will be at the mercy of family or charities. But then Americans are among the most generous of people on Earth and the outpouring of help is amazing when others are in trouble, most especially in major disasters. Chances are, somebody set up a fund or central agency to collect money and furniture or whatever for even that family who lived in the house that burned down.
It would be appropriate for the federal government to go into large disaster areas to help clear roads and administer necessary immediate emergency aid when local communities or states are overwhelmed. But that should be it. They should not assume the responsibilities that the Homewowners should have assumed in return for the privilege of home ownership.