Loadbalancing web sockets
Put a L3 load-balancer that distributes IP packets based on source-IP-port hash to your WebSocket server farm. Since the L3 balancer maintains no state (using hashed source-IP-port) it will scale to wire speed on low-end hardware (say 10GbE). Since the distribution is deterministic (using hashed source-IP-port), it will work with TCP (and hence WebSocket).
Also note that a 64k hard limit only applies to outgoing TCP/IP for a given (source) IP address. It does not apply to incoming TCP/IP. We have tested Autobahn (a high-performance WebSocket server) with 200k active connections on a 2 core, 4GB RAM VM.
Also note that you can do L7 load-balancing on the HTTP path announced during the initial WebSocket handshake. In that case the load balancer has to maintain state (which source IP-port pair is going to which backend node). It will probably scale to millions of connections nevertheless on decent setup.
Disclaimer: I am original author of Autobahn and work for Tavendo.
Note that if your websocket server logic runs on nodejs with socket.io, you can tell socket.io to use a shared redis key/value store for synchronization. This way you don't even have to care about the load balancer, events will propagate among the server instances.
var io = require('socket.io')(3000);
var redis = require('socket.io-redis');
io.adapter(redis({ host: 'localhost', port: 6379 }));
See: Socket IO - Using multiple nodes
But at some point I guess redis can become the bottleneck...