Generally applications which need to directly communicate with tens of millions of users within the space of a minute will be based on clusters of servers that have the available internet bandwidth and computational power such that they don't DoS themselves. A P2P application shouldn't require a single host to communicate with that many users, especially not within that short of a time frame.
Ray is correct that, even if you were able to send the message, you will end up DoSing yourself with the response unless you put a lot of varied-length intentional delays in the client programs to space out their responses. He's also correct that you should use UDP if you were to attempt this. I find it very unlikely that your operating system supports maintaining 10,000,000 concurrent TCP connections.
In order to send a notification to tens of millions of hosts from a single host, the original host should notify some small subset of size n of the list of tens of millions of hosts. Each of those hosts would, in turn, notify n more hosts and so on. This would require on the order of n log_n_(total number of hosts) time vs. on the order of the number of hosts time.
If the response message is simply an acknowledgement of the receipt of the original message, a system opposite this can be used for the acknowledgements. Each host can send an ack to the one that sent it the message, then once that host has received all of the acks or a timeout occurs, it sends an ack to the host that sent it the message which includes the information of which hosts have already sent it an ack. This process continues back up the tree until it the combined acks reach the original host. This means you receive on the order of n responses back to the original host, not on the order of tens of millions.
If the response is more than just an ack, then your application is probably not scalable for anything remotely close to the hardware you describe as that's going to be way too much incoming data in too short of a time. Most likely you'll DoS yourself and quite possibly get a nastygram from your ISP.