This is an interesting question about scaling in a serious situation.
You are essentially asking, "How do I establish N connections to an internet service, where N is >= 250,000".
The only way to do this effectively and efficiently is to cluster. You cannot do this on a single host, so you will need to be able to fragment and partition your client base into a number of different servers, so that each is only handling a subset.
The idea would be for a single server to hold open as few connections as possible (spreading out the connectivity evenly) while holding enough connections to make whatever service you're hosting viable by keeping inter-server communication to a minimum level. This will mean that any two connections that are related (such as two accounts that talk to each other a lot) will have to be on the same host.
You will need servers and network infrastructure that can handle this. You will need a subnet of ip addresses, each server will have to have stateless communication with the internet (i.e. your router will not be doing any NAT in order to not have to track 250,000+ connections).
You will have to talk to AOL. There is no way that AOL will be able to handle this level of connectivity without considering cutting your connection off. Any service of this scale would have to be negotiated with AOL so both you and they would be able to handle the connectivity.
There are i/o multiplexing technologies that you should investigate. Kqueue and epoll come to mind.
In order to write this massively concurrent and teleco grade solution, I would recommend investigating erlang. Erlang is designed for situations such as these (multi-server, massively-multi-client, massively-multithreaded telecommunications grade software). It is currently used for running Ericsson telephone exchanges.