When you run out of government assets, what do you do?
Government emergency managers know that the police, fire and EMS assets available to them are sized and staffed for normal day-to-day emergencies. The "official answer" to the need for a surge capability is mutual aid. Failing that, the state-to-state Emergency Management Assistance Compact (EMAC) is another means.
Enter the 21st century and there is now another whole category of first responders — citizens who are using social media to self-organize and respond to large catastrophic events, e.g., Hurricane Harvey.
Recently I became aware of CrowdSource Rescue, which is a natural evolution of volunteers wanting to become more organized themselves. Matthew Marchetti, a co-founder of CrowdSource Rescue, recently wrote me and said, "Something I always try to preach is that when faced with no alternatives, people will start turning to social media. Rumors will fly, people will request rescue, and an entire ecosystem will crop up."
Something I use in my presentations when talking about emergency managers' willingness to accept help is that, "Sometimes when you throw a rope to a drowning man, he thinks it is a snake." This is what dominates many emergency managers' thinking. They don't want one more thing to coordinate. They don't trust people they don't know. They feel as though they will lose control of the event. Liability questions may come up within the government.
To this I say, "Be willing to give up some control in order to be more effective!" Use "organized" volunteers as just another asset. Give them some priorities, direction, and let them help.
As for the average citizens — give them something to do. Tell them the best way to help is to do X. A little direction from you can help people mobilize their individual efforts to make more effective contributions. Otherwise, you get what you deserve.