I would be rather skeptical about just doing a "lets hand burgers out for free" I would like to know more details, is this a case of you just being at your church and people coming along for the food?
Now, if you are planning to make up a hundred or so burgers , wrapp them in foil and keep them warm, then go out and find where all the homless sleep and hand them out, then that would be better, knowing it went to right people instead of the rich looking for a free-load to put a few extra dollars in their bank account.
Not just the homeless, there are going to be plenty of middle class families struggling to survive, I know its bad in the UK and seen reports thats its just as bad in the USA. get in touch with food banks, law proberbly says theyc an not tell you who thier clients are, but you can prehaps ask the food bank if they can give out a leaflet or coupon from your church in their hand outs. This coupon will allow the person and their family a free meal of burger and fries each! if they turn up on the day specified. If they can not make it on the day, then just give them a frozen patty and bun etc so they can cook it at home.