Small businesses can survive in the modern economic climate. With programs like Small Business Saturday and various ad campaigns to boost the reputation of small businesses, they're thriving today. Also, with the movement of "buy local", people are flocking by the dozens to small businesses in their communities to support them.
Yes, small business can survive in the modern economic climate, if they make business decisions carefully. A small business that has a good product and a good way of marketing their product will still have customers, but it is important to make cautious business decisions, and not be over-extended. Thoughtful management can help a small business survive.