Having been on the wrong side of this equation, I can say this is exactly what they expect you to do and it's a fool's errand. I've a client on AWS faced with routine DDoS-scale spikes of traffic at certain points in the year.

The client's app almost always goes down in the midst of the fury. The point of failure typically comes down to amazon's load balancers or an auto-scaling failure. In the end our friends at amazon tell us to add more, bigger servers to 'outscale' the traffic and put the blame on us when everything blows up. sigh