I meant the latter; if your load balancers are overwhelmed how do you scale them? Further to that point, is it possible to create an architecture where load balancers are responsive and can spin up in response to traffic? If you have to deal with loads that are prone to bursts, you need to allocate those load balancers in such a way that they can handle the worst case scenario.
I haven't worked at the scale where dynamically scaling the load balancers themselves is the bottleneck. I think you pose an interesting question, and I'm hoping someone with more knowledge can comment on that.
I don't believe there is any way to scale out the ELB from user side; you can contact AWS support to 'pre warm' ELB's for high traffic sites before cutting over DNS to them.