When a site is overloaded we get an error message in return.  Why not a queue ticket instead?

Here is the real world example behind the idea:
A telecom company released a good offer and reached tens of thousands of potential users.  Soon the site was overloaded and everyone got error messages instead.  Then it gets even worse since people start reloading and increase the load even more.  Plus some customers might be irritated and skip the offer.

So:
When the site gets overloaded: pipe the requests to another server, preferably in the cloud for scaling purposes, and give people a ticket.  Ask for an email and send offers out in batches, with link to another site.  Throttle email and servers to have a steady load.  It costs more but each and one of these tens of thousands of failed requests is a potential customer.